effective digital implementation of fuzzy control systems based on approximate discrete time models this paper addresses an effective digital implementation of fuzzy control systems via an intelligent digital redesign idr approach the purpose of idr is to effectively convert an existing continuous time fuzzy controller to an equivalent sampled data fuzzy controller in the sense of the state matching the authors show that under reasonable assumptions the idr based on the exact discrete time models can be reduced to the idr based on the approximate discrete time models the state matching error between the closed loop trajectories is carefully analyzed using the integral quadratic functional approach the estimation of the state matching error is presented using the linear matrix inequality lmi techniques the problem of designing the sampled data fuzzy controller to minimize the estimation as well as to guarantee the stability is formulated and solved as the convex optimization problem with lmi constraints it is also shown that the resulting sampled data fuzzy controller recovers the performance of the continuous time fuzzy controller as the sampling period approaches zero a numerical example is used to demonstrate the effectiveness of the proposed design technique

robust stabilization of nonlinear multiple time delay large scale systems via decentralized fuzzy control to overcome the effect of modeling errors between nonlinear multiple time delay subsystems and takagi sugeno t s fuzzy models with multiple time delays a robustness design of fuzzy control is proposed in this work in terms of lyapunov s direct method a delay dependent stability criterion is hence derived to guarantee the asymptotic stability of nonlinear multiple time delay large scale systems based on this criterion and the decentralized control scheme a set of model based fuzzy controllers is then synthesized via the technique of parallel distributed compensation pdc to stabilize the nonlinear multiple time delay large scale system finally a numerical example with simulations is given to demonstrate the concepts discussed throughout this work

decentralized fuzzy observer based output feedback control for nonlinear large scale systems an lmi approach this paper presents a decentralized fuzzy control problem for asymptotic stabilization of a class of nonlinear large scale systems that use an observer based output feedback scheme a takagi sugeno t s fuzzy model is adopted for the nonlinear large scale system which has unknown interconnection terms and a fuzzy controller is separately considered for measurable and nonmeasurable premise variable cases sufficient conditions are derived for both asymptotic stabilization and optimization of a maximum bound of interconnection and are formulated in terms of linear matrix inequalities finally numerical examples are provided to verify the effectiveness of the proposed techniques

spectral properties of the transition operator associated to a multivariate refinement equation given a finitely supported sequence a on z s and an s s dilation matrix m the transition operator ta is the linear operator defined by tavoau a p b2z s aomabuvobu where a2 z s and v lies in 0oz s u the linear space of all finitely supported sequences on z s in this paper we investigate the spectral properties of the transition operator ta and apply these properties to the study of the approximation and smoothness properties of the normalized solution of the refinement equation a p a2z s aoau omau 1999

robust h filtering for sampled data fuzzy systems abstract this paper is concerned with robust h filtering for takagi sugeno sampled data fuzzy systems with uncertain parameters takagi sugeno fuzzy system can describe a wide class of nonlinear systems and is widely used in many engineering fields recently system analysis and control design for nonlinear systems based fuzzy system approach have been active the system is usually modelled as a continuous time system while in practical situations the observation is taken at discrete instants such an observation can be represented as a delayed signal first it is shown that the error system which stems from an original fuzzy system and a sampled data filter becomes a system with time varying delay sufficient conditions for the error system to achieve the robust stability with h disturbance attenuation are given in terms of linear matrix inequalities lmis we derive such conditions via output delay system approach under the assumption that sampling time is not greater than some prescribed number based on such conditions we propose a robust h sampled data filter design for a fuzzy system we consider two different cases for the premise variables in our filter design numerical examples are given to illustrate our robust h sampled data filtering

h spl infin decentralized fuzzy model reference tracking control design for nonlinear interconnected systems in general due to the interactions among subsystems it is difficult to design an h sub spl infin decentralized controller for nonlinear interconnected systems the model reference tracking control problem of nonlinear interconnected systems is studied via h sub spl infin decentralized fuzzy control method first the nonlinear interconnected system is represented by an equivalent takagi sugeno type fuzzy model a state feedback decentralized fuzzy control scheme is developed to override the external disturbances such that the h spl infin model reference tracking performance is achieved furthermore the stability of the nonlinear interconnected systems is also guaranteed if states are not all available a decentralized fuzzy observer is proposed to estimate the states of each subsystem for decentralized control consequently a fuzzy observer based state feedback decentralized fuzzy controller is proposed to solve the h sub spl infin tracking control design problem for nonlinear interconnected systems the problem of h sub spl infin decentralized fuzzy tracking control design for nonlinear interconnected systems is characterized in terms of solving an eigenvalue problem evp the evp can be solved very efficiently using convex optimization techniques finally simulation examples are given to illustrate the tracking performance of the proposed methods

nonlinear decentralized state feedback controller for uncertain fuzzy time delay interconnected systems abstract in this paper the perturbed continuous time interconnected system with time delay is represented by an equivalent takagi sugeno type fuzzy model having r i rules for each subsystem based on lyapunov stability theorem and razumikhin theorem the nonlinear decentralized state feedback fuzzy controllers are proposed to stabilize the whole perturbed fuzzy time delay interconnected system asymptotically under using this nonlinear controller the design methods only consider the r i fuzzy rules rather than r i r i rules for each subsystem that is we can remove the negative effect of the coupled terms therefore these approaches can be less conservative moreover if all the time delays of each subsystem are the same for all rules we shall propose less conservative criteria these criteria do not need the solution of a lyapunov equation or a riccati equation we also do not need to find a common positive matrix p to satisfy any inequality the so called matching condition for the interconnection matrices and perturbations are not needed finally a numerical example is given to illustrate the control design and its effectiveness

analysis of non isentropic compressible euler equations with relaxation abstract this paper is contributed to the study of the one dimensional non isentropic compressible euler equations with relaxation it is shown that classical solutions do not exist globally in time under general conditions on initial data indeed finite time blowup occurs in a quantity related to the first moment on the other hand when the initial datum is sufficiently close to a constant equilibrium state it is shown that the equations possess a unique global in time classical solution and the solution converges to the equilibrium state in the long time run when the domain is finite the convergence rate is shown to be exponential due to boundary effects

stability analysis and design of fuzzy control systems abstract the stability analysis and the design technique of fuzzy control systems using fuzzy block diagrams are discussed first we show the concept of fuzzy blocks and consider the connection problems of fuzzy blocks diagrams we derive some theorems and corollaries with respect to two basic types of connections of fuzzy blocks in order to preserve some properties in a connection of fuzzy blocks continuous piecewise polynomial membership functions are defined secondly a sufficient condition which guarantees the stability of fuzzy systems is obtained in terms of lyapunov s direct method we give an important fact based on this condition thirdly we propose a new design technique of a fuzzy controller the fuzzy block diagrams and the stability analysis are applied to the design problems of a model based fuzzy controller

adaptive fuzzy control for full states constrained systems with nonstrict feedback form and unknown nonlinear dead zone this paper addresses the problem of direct adaptive fuzzy tracking control design for a class of uncertain nonstrict feedback systems with nonlinear dead zone and full state constraints fuzzy logic systems are used to approximate some unknown nonlinear functions and less adjustable parameters are adopted in each backstepping design process this advantage is first to take into account the full state constrained nonstrict feedback systems with input dead zone nonlinearity to guarantee that the full state constraints are not violated a novel adaptive fuzzy controller is developed by introducing barrier lyapunov function with the error variables furthermore it is proved that all the closed loop signals remain semi globally uniformly ultimately bounded and the tracking error converges to a small neighborhood of the origin two simulation examples are provided to verify the effectiveness of the proposed control method

triangular 7 and quadrilateral 5 subdivision schemes regular case abstract this paper is devoted to the study of triangular 7 and quadrilateral 5 surface subdivisions both approximation and interpolatory subdivision schemes are considered with illustrative examples of both scalar valued and matrix valued 7 and 5 subdivision masks that satisfy the sum rule of sufficiently high orders in particular optimal sobolev smoothness is determined and holder smoothness estimates are presented

intelligent digital redesign revisited approximate discretization and stability limitation this paper sharpens the recently developed intelligent digital redesign idr technique in regard of stability a major assumption in the previous result was that the firing strength of each fuzzy rule is approximated as its sampled value during a sampling period for efficient discretization of the takagi sugeno t s fuzzy system by which some unexpected stability might be experienced for certain sampling period as large as the assumption is unrealistic to clarify results for that case we refine the idr condition and prove that the uniformly semiglobal practical asymptotic stability of the sampled data t s fuzzy control system by the intelligently redesigned digital fuzzy controller rather than the global exponential stability shown in the previous result

multirate robust digital control for fuzzy systems with periodic lyapunov function sampled data control which is capable of stabilizing general nonlinear systems is of great current interest in this paper the takagi sugeno ts fuzzy model is used to represent the nonlinear plant the paper is primarily concerned with designing digital controllers for the ts fuzzy continuous time model to stabilize the closed loop system in the problem formulation we only assume that the sampled values at a sampling rate of 1 t sub s are available for control within the sampling intervals the fuzzy controller uses the sampled data at the sampling instants to fire a fuzzy rule and generate a digital control action series this digital control action is then fed into the nonlinear system through a zero order holder in this paper two kinds of digital controllers are designed multirate and single rate digital controllers within a sampling interval the single rate controller is static while the multirate controller is periodically time varying i e the control action is switched at a small switching period t clearly for the single rate case this switching period t is equal to the sampling period t sub s this paper presents a design procedure for the multirate fuzzy controller with the single rate control as a special case the results are formulated as linear matrix inequalities numerical example shows the effectiveness of the proposed design procedures

novel delay dependent robust h control of uncertain systems with distributed time varying delays this paper investigates the problem of delay dependent robust h control for a class of uncertain systems with distributed time varying delays the aim is to design a delay dependent robust h control which ensures robust asymptotic stability of the system the delay derivative dependent robust h control criteria are obtained in terms of linear matrix inequalities lmis numerical examples are given to illustrate the effectiveness of the proposed method the results are also compared with the existing results to show the conservativeness

lmi based relaxed nonquadratic stabilization conditions for nonlinear systems in the takagi sugeno s form this paper presents the stabilization analysis for a class of nonlinear systems that are represented by a takagi and sugeno ts discrete fuzzy model takagi and sugeno ieee trans systems man cybern 15 1 1985 116 the main result given here concerns their stabilization using new control laws and new nonquadratic lyapunov functions new relaxed conditions and linear matrix inequality based design are proposed that allow outperforming previous results found in the literature two examples are also provided to demonstrate the efficiency of the approaches

approximation properties of multivariate wavelets wavelets are generated from refinable functions by using multiresolution analysis in this paper we investigate the approximation properties of multivariate refinable functions we give a characterization for the approximation order provided by a refinable function in terms of the order of the sum rules satisfied by the refinement mask we connect the approximation properties of a refinable function with the spectral properties of the corresponding subdivision and transition operators finally we demonstrate that a refinable function in w k 1 1 r s provides approximation order k

robust h stabilization for t s fuzzy systems with time varying delays and memory sampled data control abstract in this paper we address the robust h stabilization for t s fuzzy systems with time varying delays based on memory sampled data control by developing some new terms an improved piecewise lyapunov krasovskii functional lkf is constructed to take full advantage of characteristic about real sampling pattern furthermore some relaxed matrices proposed in the lkf are not necessarily positive definite by using the lkf and free matrix based fmb integral inequality some sufficient criteria are established to ensure the stability of fuzzy systems and reduce the influence of external disturbance with an h norm bound then the memory sampled data controller can be derived by solving a group of linear matrix inequalities lmis with the maximal sampling period finally a numerical example is given to demonstrate the benefits and the superiority of the approach proposed

mammographic feature enhancement by multiscale analysis introduces a novel approach for accomplishing mammographic feature analysis by overcomplete multiresolution representations the authors show that efficient representations may be identified within a continuum of scale space and used to enhance features of importance to mammography methods of contrast enhancement are described based on three overcomplete multiscale representations 1 the dyadic wavelet transform separable 2 the spl phi transform nonseparable nonorthogonal and 3 the hexagonal wavelet transform nonseparable multiscale edges identified within distinct levels of transform space provide local support for image enhancement mammograms are reconstructed from wavelet coefficients modified at one or more levels by local and global nonlinear operators in each case edges and gain parameters are identified adaptively by a measure of energy within each level of scale space the authors show quantitatively that transform coefficients modified by adaptive nonlinear operators can make more obvious unseen or barely seen features of mammography without requiring additional radiation the authors results are compared with traditional image enhancement techniques by measuring the local contrast of known mammographic features they demonstrate that features extracted from multiresolution representations can provide an adaptive mechanism for accomplishing local contrast enhancement by improving the visualization of breast pathology one can improve chances of early detection while requiring less time to evaluate mammograms for most patients

convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping we consider a model of hyperbolic conservation laws with damping and show that the solutions tend to those of a nonlinear parabolic equation time asymptotically the hyperbolic model may be viewed as isentropic euler equations with friction term added to the momentum equation to model gas flow through a porous media in this case our result justifies darcy s law time asymptotically our model may also be viewed as an elastic model with damping

orthogonal and biorthogonal fir hexagonal filter banks with sixfold symmetry recently hexagonal image processing has attracted attention the hexagonal lattice has several advantages in comparison with the rectangular lattice the conventionally used lattice for image sampling and processing for example a hexagonal lattice needs less sampling points it has better consistent connectivity it has higher symmetry and its structure is plausible to human vision systems the multiresolution analysis method has been used for hexagonal image processing since the hexagonal lattice has high degree of symmetry it is desirable that the hexagonal filter banks designed for multiresolution hexagonal image processing also have high order of symmetry which is pertinent to the symmetry structure of the hexagonal lattice the orthogonal or prefect reconstruction pr hexagonal filter banks that are available in the literature have only threefold symmetry in this paper we investigate the construction of orthogonal and pr finite impulse response fir hexagonal filter banks with sixfold symmetry we obtain block structures of 7 size refinement seven channel two dimensional orthogonal and pr fir hexagonal filter banks with sixfold rotational symmetry radic7 refinement orthogonal and biorthogonal wavelets based on these block structures are constructed in this paper we also consider fir hexagonal filter banks with axial line symmetry and we present a block structure of fir hexagonal filter banks with pseudo sixfold axial symmetry

stability analysis and performance design for fuzzy model based control system under imperfect premise matching this paper investigates the stability analysis and performance design of nonlinear systems to facilitate the stability analysis the takagi sugeno t s fuzzy model is employed to represent the nonlinear plant under the imperfect premise matching in which t s fuzzy model and fuzzy controller do not share the same membership functions a fuzzy controller with enhanced design flexibility and robustness property is proposed to control the nonlinear plant however the nice characteristic given by the perfect premise matching leading to conservative stability conditions vanishes in this paper under the imperfect premise matching information of membership functions of the fuzzy model and controller are considered in stability analysis with the introduction of slack matrices relaxed linear matrix inequality lmi based stability conditions are derived using lyapunov based approach furthermore lmi based performance conditions are provided to guarantee system performance simulation examples are given to illustrate the effectiveness of the proposed approach

fingerprint classification using a hexagonal fast fourier transform in this paper a new method for the analysis of fingerprint images is presented a hexagonal fourier transform is applied that will classify fingerprints into whorls loops and arches the hexagonal fourier transform allows the utilization of hexagonally sampled data and the extention of output data in a rectangular scheme which is more convenient for treatment and interpretation results for fingerprint classification are given

fuzzy stabilization of nonlinear systems under sampled data feedback an exact discrete time model approach this paper addresses stabilization problems for a nonlinear system via a sampled data fuzzy controller the nonlinear system is assumed to be exactly modeled in takagi sugeno s form at least locally unlike the conventional direct discrete time design approach based on an approximate discrete time model the sampled data fuzzy controllers are designed based on an exact discrete time model sufficient design conditions are formulated in terms of linear matrix inequalities it is shown that whenever the exact discrete time fuzzy model is asymptotically stabilizable via the sampled data fuzzy controller uniformly bounded in the state then so is the original nonlinear system a numerical example is given to illustrate the effectiveness of the proposed methodology

decentralized sampled data h fuzzy filter for nonlinear large scale systems this paper presents a decentralized sampled data h fuzzy filter design method for nonlinear large scale systems which are represented by a takagi sugeno t s fuzzy model based on the t s fuzzy model the error system between the nonlinear large scale system and the filter is obtained the discretization process of the error system is accomplished with the exact discrete time approach to eliminate the exact approximate mismatch by using the discrete time lyapunov sense the sufficient condition of the asymptotic stability for the error system is given and a prescribed level of the h norm is ensured to guarantee the h fuzzy filter performance finally numerical examples are given to show the effectiveness of the proposed methods

critical thresholds in 2d restricted euler poisson equations we provide a complete description of the critical threshold phenomenon for the two dimensional localized euler poisson equations introduced by the authors in comm math phys 228 2002 pp 435 466 here the questions of global regularity vs finite time breakdown for the two dimensional 2d restricted euler poisson solutions are classified in terms of precise explicit formulae describing a remarkable variety of critical threshold surfaces of initial configurations in particular it is shown that the 2d critical thresholds depend on the relative sizes of three quantities the initial density the initial divergence and the initial spectral gap that is the difference between the two eigenvalues of the 2 2 initial velocity gradient

orthogonal and biorthogonal sqrt 3 refinement wavelets for hexagonal data processing the hexagonal lattice was proposed as an alternative method for image sampling the hexagonal sampling has certain advantages over the conventionally used square sampling hence the hexagonal lattice has been used in many areas a hexagonal lattice allows radic3 dyadic and radic7 refinements which makes it possible to use the multiresolution multiscale analysis method to process hexagonally sampled data the radic3 refinement is the most appealing refinement for multiresolution data processing due to the fact that it has the slowest progression through scale and hence it provides more resolution levels from which one can choose this fact is the main motivation for the study of radic3 refinement surface subdivision and it is also the main reason for the recommendation to use the radic3 refinement for discrete global grid systems however there is little work on compactly supported radic3 refinement wavelets in this paper we study the construction of compactly supported orthogonal and biorthogonal radic3 refinement wavelets in particular we present a block structure of orthogonal fir filter banks with twofold symmetry and construct the associated orthogonal radic3 refinement wavelets we study the sixfold axial symmetry of perfect reconstruction biorthogonal fir filter banks in addition we obtain a block structure of sixfold symmetric radic3 refinement filter banks and construct the associated biorthogonal wavelets

delay dependent guaranteed cost control for t s fuzzy systems with time delays this study introduces a guaranteed cost control method for nonlinear systems with time delays which can be represented by takagi sugeno t s fuzzy models with time delays the state feedback and generalized dynamic output feedback approaches are considered the generalized dynamic output feedback controller is presented by a new fuzzy controller architecture which is of dual indexed rule base it considers both the dynamic part and the output part of t s fuzzy model which guarantees that the controller without any delay information can stabilize time delay t s fuzzy systems based on delay dependent lyapunov functional approach some sufficient conditions for the existence of state feedback controller are provided via parallel distributed compensation pdc first second the corresponding conditions are extended into the generalized dynamic output feedback closed loop system via so called generalized pdc technique the upper bound of time delay can be obtained using convex optimization such that the system can be stabilized for all time delays whose sizes are not larger than the bound the minimizing method is also proposed to search the suboptimal upper bound of guaranteed cost function the effectiveness of the proposed method can be shown by the simulation examples

decentralized h fuzzy filter for nonlinear large scale sampled data systems with uncertain interconnections abstract this paper proposes a decentralized h fuzzy filter technique for nonlinear large scale interconnected systems that are based on the takagi sugeno fuzzy model the large scale system has unknown interconnection terms that are assumed to satisfy the quadratic bounds an error system between the nonlinear large scale system and the decentralized filter is constructed by using the fuzzy lyapunov technique sufficient conditions are proposed for both showing asymptotic stability and guaranteeing h fuzzy filter performance these sufficient conditions are derived in terms of linear matrix inequalities finally simulation examples are given to demonstrate the effectiveness of the proposed technique

a novel approach to h_ bm infty decentralized fuzzy observer based fuzzy control design for nonlinear interconnected systems in general due to the interactions among subsystems it is difficult to design an h infin decentralized output feedback controller for nonlinear interconnected systems this study introduces h infin decentralized fuzzy observer based fuzzy control design where the premise variables depend on the state variables estimated by a fuzzy observer for nonlinear interconnected systems via t s fuzzy models the fuzzy control design for this case is more flexible but much more complex than that for the case where the premise variables depend on the state variables only a novel decoupled method is proposed in this study to transform the non linear matrix inequality non lmi conditions into some lmi forms by the proposed decoupled method the problem of h infin decentralized fuzzy observer based fuzzy control design for nonlinear interconnected systems is characterized in terms of solving an eigenvalue problem evp with five prespecified scalars for each subsystem in general it is a difficult task to solve the evp with five prespecified scalars fortunately this special evp can be easily solved by using a genetic algorithm and an lmi based optimization method finally a simulation example is given to illustrate the design procedure and robust performance of the proposed methods

multiresolution analysis haar bases and self similar tilings of r sup n orthonormal bases for l sup 2 r sup n are constructed that have properties that are similar to those enjoyed by the classical haar basis for l sup 2 r for example each basis consists of appropriate dilates and translates of a finite collection of piecewise constant functions the construction is based on the notion of multiresolution analysis and reveals an interesting connection between the theory of compactly supported wavelet bases and the theory of self similar tilings

new approaches to relaxed quadratic stability condition of fuzzy control systems this paper deals with the quadratic stability conditions of fuzzy control systems that relax the existing conditions reported in the previous literatures two new conditions are proposed and shown to be useful in analyzing and designing fuzzy control systems the first one employs the s procedure to utilize information regarding the premise parts of the fuzzy systems the next one enlarges the class of fuzzy control systems whose stability is ensured by representing the interactions among the fuzzy subsystems in a single matrix and solving it by linear matrix inequality the relationships between the suggested stability conditions and the conventional well known stability conditions reported in the previous literatures are also discussed and it is shown in a rigorous manner that the second condition of this paper includes the conventional conditions finally some examples and simulation results are presented to illustrate the effectiveness of the stability conditions

stabilization of nonlinear systems under variable sampling a fuzzy control approach this paper investigates the problem of stabilization for a takagi sugeno t s fuzzy system with nonuniform uncertain sampling the sampling is not required to be periodic and the only assumption is that the distance between any two consecutive sampling instants is less than a given bound by using the input delay approach the t s fuzzy system with variable uncertain sampling is transformed into a continuous time t s fuzzy system with a delay in the state though the resulting closed loop state delayed t s fuzzy system takes a standard form the existing results on delay t s fuzzy systems cannot be used for our purpose due to their restrictive assumptions on the derivative of state delay a new condition guaranteeing asymptotic stability of the closed loop sampled data system is derived by a lyapunov approach plus the free weighting matrix technique based on this stability condition two procedures for designing state feedback control laws are given one casts the controller design into a convex optimization by introducing some over design and the other utilizes the cone complementarity linearization idea to cast the controller design into a sequential minimization problem subject to linear matrix inequality constraints which can be readily solved using standard numerical software an illustrative example is provided to show the applicability and effectiveness of the proposed controller design methodology

parameterized linear matrix inequality techniques in fuzzy control system design this paper proposes different parameterized linear matrix inequality plmi characterizations for fuzzy control systems these plmi characterizations are in turn relaxed into pure lmi programs which provides tractable and effective techniques for the design of suboptimal fuzzy control systems the advantages of the proposed methods over earlier ones are then discussed and illustrated through numerical examples and simulations

sampled data robust h control for t s fuzzy systems with time delay and uncertainties abstract this paper investigates sampled data robust h control for t s fuzzy systems with time delay and uncertainties by introducing the free weighting matrices to deal with the integral items and converting the coupling time varying matrix inequalities into a group of decoupling matrix inequalities an innovative delay dependent stabilization criterion is first presented then a sampled data h controller is designed to stabilize the t s fuzzy system to achieve the prescribed disturbance attenuation level which is dependent on both the size of state delay and upper bound of allowable sampling period since 1 the sawtooth structure of delay is fully considered 2 neither model transformation nor bounding techniques are employed in deriving the delay dependent results and 3 none of the integral items are arbitrarily ignored and magnified the less conservative results can be expected a practical application example is given to demonstrate the effectiveness of the proposed methods

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

critical thresholds in hyperbolic relaxation systems article history received 8 august 2008 available online 18 april 2009 critical threshold phenomena in one dimensional 2 2q uasi linear hyperbolic relaxation systems are investigated assuming both the subcharacteristic condition and genuine nonlinearity of the flux we prove global in time regularity and finite time singularity formation of solutions simultaneously by showing the critical threshold phenomena associated with the underlying relaxation systems our results apply to the well known isentropic euler system with damping within the same framework it is also shown that the solution of the semi linear relaxation system remains smooth for all time provided the subcharacteristic condition is satisfied

asymptotic behavior of solutions for p system with relaxation in this paper we consider the asymptotic behavior of solutions for the cauchy problem for p system with relaxationvt ux 0 ut p v x 1e f v u e with initial data v u x 0 v 0 x u 0 x v u v 0 asx i we are interested to show the solutions of e i tend also to the equilibrium rarefaction waves and the traveling waves even if the limits v u of the initial data at x do not satisfy the equilibrium equation i e u f v when the limits of the initial data at infinity satisfy equilibrium states liu 9 studied the stability of rarefaction waves and traveling waves for the general 2 2 hyperbolic conservation laws with relaxation

fuzzy adaptive decentralized output feedback control for large scale nonlinear systems with dynamical uncertainties in this paper an adaptive fuzzy decentralized robust output feedback control approach is proposed for a class of large scale strict feedback nonlinear systems with the unmeasured states the large scale nonlinear systems in this paper are assumed to possess the unstructured uncertainties unmodeled dynamics and unknown high frequency gain sign fuzzy logic systems are used to approximate the unstructured uncertainties k filters are designed to estimate the unmeasured states and a dynamical signal and a special nussbaum gain function are introduced into the control design to solve the problem of unknown high frequency gain sign and dominate unmodeled uncertainties respectively based on the backstepping design and adaptive fuzzy control methods an adaptive fuzzy decentralized robust output feedback control scheme is developed it is proved that the proposed adaptive fuzzy control approach can guarantee that all the signals in the closed loop system are uniformly and ultimately bounded and the tracking errors converge to a small neighborhood of the origin the effectiveness of the proposed approach is illustrated by using simulation results

a new intelligent digital redesign for t s fuzzy systems global approach this paper proposes a novel and efficient global intelligent digital redesign technique for a takagi sugeno t s fuzzy system the term of intelligent digital redesign involves converting an existing analog fuzzy model based controller into an equivalent digital counterpart in the sense of state matching the proposed method should be notably discriminated from the previous works in that it allows us to globally match the states of the overall closed loop t s fuzzy system with the predesigned analog fuzzy model based controller and those with the digitally redesigned fuzzy model based controller and further to examine the stabilizability by the redesigned controller in the sense of lyapunov the key idea is that the global intelligent digital redesign problem is viewed as a convex minimization problem of the norm distance between nonlinearly interpolated linear operators to be matched sufficient conditions for the global state matching and the stability of the digitally controlled system are formulated in terms of linear matrix inequalities lmis a complex nonlinear system duffing like chaotic oscillator is simulated and demonstrated to validate the feasibility and effectiveness of the proposed digital redesign technique which implies the safe applicability to the digital control system

convergence to equilibrium for the relaxation approximations of conservation laws we study the cauchy problem for 2 2 semilinear and quasilinear hyperbolic systems with a singular relaxation term special comparison and compactness properties are established by assuming the subcharacteristic condition therefore we can prove the convergence to equilibrium of the solutions of these problems as the singular perturbation parameter tends to 0 this research was strongly motivated by the recent numerical investigations of s jin and z xin on the relaxation schemes for conservation laws 1996 john wiley sons inc

cauchy problem for an isentropic magnetogasdynamic system abstract this paper investigates the cauchy problem for an isentropic magnetogasdynamic system under certain reasonable hypotheses on the initial data we obtain the global existence and uniqueness of the c 1 solution to the system meanwhile when the hypotheses on the initial data do not hold we obtain the blow up phenomena of the c 1 solution to the system the bounds of the solution are shown to depend on the parameter which characterizes a one dimensional plane flow 0 or a three dimensional cylindrically symmetric flow 1 it is shown that the existence of the finite time singularity is significantly influenced by the magnetic field strength present in the flow along with the initial data

hex splines a novel spline family for hexagonal lattices this paper proposes a new family of bivariate nonseparable splines called hex splines especially designed for hexagonal lattices the starting point of the construction is the indicator function of the voronoi cell which is used to define in a natural way the first order hex spline higher order hex splines are obtained by successive convolutions a mathematical analysis of this new bivariate spline family is presented in particular we derive a closed form for a hex spline of arbitrary order we also discuss important properties such as their fourier transform and the fact they form a riesz basis we also highlight the approximation order for conventional rectangular lattices hex splines revert to classical separable tensor product b splines finally some prototypical applications and experimental results demonstrate the usefulness of hex splines for handling hexagonally sampled data

sub hexagonal phase correlation for motion estimation we present a novel frequency domain motion estimation technique which operates on hexagonal images and employs the hexagonal fourier transform our method involves image sampling on a hexagonal lattice followed by a normalised hexagonal cross correlation in the frequency domain the term subpixel or subcell is defined on a hexagonal grid in order to achieve floating point registration experiments using both artificially induced motion and actual motion demonstrate that the proposed method outperforms the state of the art in frequency domain motion estimation operating on a square lattice in the shape of phase correlation in terms of subpixel accuracy for a range of test material and motion scenarios

sampled data h fuzzy filtering for nonlinear systems with missing measurements in this paper a sampled data h fuzzy filtering problem is considered for nonlinear systems with missing measurements the nonlinear sampled data system and missing measurements are assumed to be represented by a takagisugeno ts fuzzy system and an independent identically distributed bernoulli random process respectively based on the fuzzy system the h fuzzy filtering problem is formulated to design the sampled data fuzzy filter by using the exponential mean square stability definition the stability condition with an h performance is guaranteed for the fuzzy system with the sampled data fuzzy filter and its sufficient condition is converted into the linear matrix inequality lmi format finally an example is provided to verify the effectiveness of the proposed fuzzy filtering technique

gas dynamics in thermal nonequilibrium and general hyperbolic systems with relaxation we study gas flow in vibrational nonequilibrium the model is a 4 4 nonlinear hyperbolic system with relaxation under physical assumptions properties of thermodynamic variables relevant to stability are obtained global existence for cauchy problems with smooth and small data is established and large time behavior is studied in the pointwise sense we formulate the fundamental solution in a systematic way for a general linear system with relaxation the fundamental solution provides insights to the behavior of the nonlinear system and is crucial to obtain our pointwise asymptotic picture for the nonequilibrium flow we also clarify in a general setting the relation between subcharacteristic conditions and a dissipative criterion that was originally proposed for hyperbolic parabolic systems and has now proved to be important also for hyperbolic systems with relaxation

sampled data observer based output feedback fuzzy stabilization of nonlinear systems exact discrete time design approach this paper presents a new direct discrete time design methodology of a sampled data observer based output feedback fuzzy controller for a class of nonlinear system that is exactly modeled in takagi sugeno s form at least locally a fundamental yet challenging issue in this direction is the unavailability of the exact discrete time model of the nonlinear plant in a closed form in contrast to the earlier works that are based on an approximate discrete time model thus the stability obtained in the design step is not preserved in the implementation step we employ an exact discrete time fuzzy model in an integral form sufficient asymptotic stabilization conditions are investigated in the discrete time lyapunov sense we then show that the resulting sampled data controller indeed asymptotically stabilizes the nonlinear plant an example is provided to illustrate the effectiveness of the proposed methodology

brief paper stability connection between sampled data fuzzy control systems with quantization and their approximate discrete time model this paper concerns the stability of a sampled data takagi sugeno t s fuzzy control system with quantization when a controller design is based on an approximate discrete time model of the plant without quantization the motivations come from the facts that digital devices for interfacing a plant with a controller quantize signals and an exact discrete time model of the t s fuzzy system is generally not amenable to synthesis process we show that the concerned system is lagrange stabilizable by the controller asymptotically stabilizing the approximate discrete time model a constructive design algorithm for the developed stability analysis is proposed in terms of linear matrix inequalities

robust reliable h control for fuzzy systems with random delays and linear fractional uncertainties this article studies the reliable robust stabilization problem for a class of uncertain takagi sugeno ts fuzzy systems with time varying delays the delay factor is assumed to be random delay which belongs to a given interval and parameter uncertainties are considered with linear fractional transformation form by implementing a proper novel lyapunov functional together with linear matrix inequality lmi approach a new set of delay dependent sufficient conditions is derived to guarantee the asymptotic stability of ts fuzzy system with a prescribed h performance index further a reliable robust h control design with an appropriate gain matrix has been derived to achieve the robust asymptotic stability for uncertain ts fuzzy system further schur complement and jensen s integral inequality are used to simplify the derivation in the main results the set of sufficient conditions is established using the relationship among the random time varying delay and its lower and upper bounds which can be easily solved by matlab lmi toolbox finally an illustrative example based on the truck trailer model is provided to show the effectiveness of the proposed new design technique

interval type 2 fuzzy tracking control for nonlinear systems via sampled data controller abstract this paper addresses an interval type 2 it2 fuzzy sampled data tracking control problem of nonlinear systems subject to uncertain parameters the controlled plant is modeled as takagi sugeno t s fuzzy structure where the parameter uncertainties are captured effectively by the lower and upper membership functions by means of the linear matrix inequalities lmis and free weighting matrices an it2 fuzzy sampled data control scheme is developed such that the system states are driven to track those of the reference model finally an inverted pendulum system and a mass spring damper mechanical system are used to show the efficiency of the suggested tracking control design

triangular 3 subdivision schemes the regular case the paper deals with the investigation of triangular 3 subdivision schemes in the stationary shift invariant setting in section 2 we collect the available theory on refinable functions subdivision surfaces with emphasis on their sobolev and holder smoothness families of interpolatory and approximating 3 subdivision schemes are investigated in section 3 some dual 3 subdivision schemes which are related to vector valued refinable functions are also analyzed for this purpose we have developed matlab routines for numerically investigating properties of vector subdivision schemes

rotation prevents finite time breakdown we consider a two dimensional 2d convection model augmented with the rotational coriolis forcing ut u xu 2ku w ith afi xed 2k being the inverse rossby number we ask whether the action of dispersive rotational forcing alone u prevents the generic finite time breakdown of the free nonlinear convection the answer provided in this work is a conditional yes namely we show that the rotating euler equations admit global smooth solutions for a subset of generic initial configurations with other configurations however finite time breakdown of solutions may and actually does occur thus global regularity depends on whether the initial configuration crosses an intrinsic o 1 critical threshold ct which is quantified in terms of the initial vorticity 0 u0 and the initial spectral gap associated with the 2 2 initial velocity gradient 0 2 0 1 0 j 0 j u0 specifically global regularity of the rotational euler equation is ensured if and only if 4k 0 2 4k 2 r 2 we also prove that the velocity field remains smooth if and only if it is periodic an equivalent lagrangian formulation reconfirms the ct and shows a global periodicity of velocity field as well as the associated particle orbits moreover we observe yet another remarkable periodic behavior exhibited by the gradient of the velocity field the spectral dynamics of the eulerian formulation siam j math anal 33 2001 930 reveals that the vorticity and the divergence of the flow evolve with their own path dependent period we conclude with a kinetic formulation of the rotating euler equation 2003 elsevier b v all rights reserved msc 35q35 35b30

optimal multifilter banks design related symmetric extension transform and application to image compression the design of optimal multifilter banks and optimum time frequency resolution multiwavelets with different objective functions is discussed the symmetric extension transform related to multifilter banks with symmetric properties is presented it is shown that such a symmetric extension transform is nonexpensive more optimal multifilter banks for image compression are constructed and some of them are used in image compression experiments show that optimal multifilter banks have better performances in image compression than daubechies orthogonal wavelet filters and daubechies least asymmetric wavelet filters and for some images they even have better performances than the scalar 9 7 tap biorthogonal wavelet filters experiments also show that the symmetric extension transform provided in this paper improves the rate distortion performance compared with the periodic extension transform

hyperbolic conservation laws with stiff relaxation terms and entropy we study the limiting behavior of systems of hyperbolic conservation laws with stiff relaxation terms reduced systems inviscid and viscous local conservation laws and weakly nonlinear limits are derived through asymptotic expansions an entropy condition is introduced for n n systems that ensures the hyperbolicity of the reduced inviscid system the resulting characteristic speeds are shown to be interlaced with those of the original system moreover the first correction to the reduced system is shown to be dissipative a partial converse is proved for 2 2 systems this structure is then applied to study the convergence to the reduced dynamics for the 2 2 case 1994 john wiley sons inc

spectral dynamics of the velocity gradient field in restricted flows we study the velocity gradients of the fundamental eulerian equation t u u u f which shows up in different contexts dictated by the different modeling of f s to this end we utilize a basic description for the spectral dynamics of u expressed in terms of the possibly complex eigenvalues u which are governed by the ricatti like equation t u 2 l fr we focus our investigation on four prototype models associated with different forcing f ranging from simple linear damping and viscous dusty medium models to the main thrust of the paper the restricted models of euler navier stokes equations and euler poisson equations in particular we address the question of the time regularity for these models that is whether they admit a finite time breakdown a global smooth solution or an intermediate scenario of critical threshold phenomena where global regularity depends on initial configurations using the spectral dynamics as our essential tool in these investigations we obtain a simple form of a critical threshold for the linear damping model and we identify the 2d vanishing viscosity limit for the viscous irrotational dusty medium model moreover for the n dimensional restricted euler equations we obtain n 2 1 global invariants interesting for their own sake which enable us to precisely characterize the local topology at breakdown time extending previous studies in the n 3 dimensional case finally as a fourth model we introduce the n dimensional restricted euler poisson rep system identifying a set of n 2 global invariants which in turn yield i sufficient conditions for finite time breakdown and ii characterization of a large class of 2 dimensional

fir filter banks for hexagonal data processing images are conventionally sampled on a rectangular lattice thus traditional image processing is carried out on the rectangular lattice the hexagonal lattice was proposed more than four decades ago as an alternative method for sampling compared with the rectangular lattice the hexagonal lattice has certain advantages which include that it needs less sampling points it has better consistent connectivity and higher symmetry the hexagonal structure is also pertinent to the vision process in this paper we investigate the construction of symmetric fir hexagonal filter banks for multiresolution hexagonal image processing we obtain block structures of fir hexagonal filter banks with 3 fold rotational symmetry and 3 fold axial symmetry these block structures yield families of orthogonal and biorthogonal fir hexagonal filter banks with 3 fold rotational symmetry and 3 fold axial symmetry in this paper we also discuss the construction of orthogonal and biorthogonal fir filter banks with scaling functions and wavelets having optimal smoothness in addition we present a few of such orthogonal and biorthogonal fir filters banks

global existence of smooth solutions for partially dissipative hyperbolic systems with a convex entropy we consider the cauchy problem for a general one dimensional n n hyperbolic symmetrizable system of balance laws it is well known that in many physical examples for instance for the isentropic euler system with damping the dissipation due to the source term may prevent the shock formation at least for smooth and small initial data our main goal is to find a set of general and realistic sufficient conditions to guarantee the global existence of smooth solutions and possibly to investigate their asymptotic behavior for systems which are entropy dissipative a quite natural generalization of the kawashima condition for hyperbolic parabolic systems can be given in this paper we first propose a general framework for this kind of problem by using the so called entropy variables then we go on to prove some general statements about the global existence of smooth solutions under different sets of conditions in particular the present approach is suitable for dealing with most of the physical examples of systems with a relaxation extension our main tools will be some refined energy estimates and the use of a suitable version of the kawashima condition

stability analysis and stabilization of fuzzy state space models abstract a new stability test method for linguistic fuzzy state space models is proposed in this paper this method allows the determination of stability of fuzzy models by applying the lyapunov function to each rule a gradient based algorithm is suggested to simplify the stability tests using this algorithm the lyapunov equation can be updated towards the direction where the stability can be determined more correctly an additional gradient based stabilizing algorithm is also derived which allows a systematic approach to find stabilizing controls by updating the lyapunov equations towards the direction where unstable eigenvalues are decreased examples demonstrate the convenience of the stability test and the two suggested gradient based algorithms

hierarchical subsampling giving fractal regions recursive image subsampling which yields support areas approaching fractals is described and analyzed using iterated function systems the subsampling scheme is suitable in e g hierarchical image processing and image coding schemes for hexagonally sampled images a hierarchical subsampling structure is given which yields hexagon like regions with fractal borders

digitalizing a fuzzy observer based output feedback control intelligent digital redesign approach this paper concerns an intelligent digital redesign idr technique for a takagi sugeno fuzzy observer based output feedback control fobofc system the term idr involves converting an existing analog control into an equivalent digital counterpart in the sense of state matching the idr problem is herein viewed as a minimization problem of the norm distances between nonlinearly interpolated linear operators to be matched its constructive condition with global rather than local state matching is formulated in terms of bilinear matrix inequalities the main features of the proposed method are that the state estimation error in the plant dynamics is considered in the idr condition that plays a crucial role in the performance improvement the stability property is preserved by the proposed idr algorithm the separation principle is shown when the premise variables are measurable finally the idr condition for a more general fobofc an estimated premise variable case is conducted a numerical example is demonstrated to visualize the feasibility of the developed methodology

a new discrete time robust stability condition a new robust stability condition for uncertain discrete time systems with convex polytopic uncertainty is given it enables to check stability using parameter dependent lyapunov functions which are derived from lmi conditions it is shown that this new condition provides better results than the classical quadratic stability besides the use of a parameter dependent lyapunov function this condition exhibits a kind of decoupling between the lyapunov and the system matrices which may be explored for control synthesis purposes a numerical example illustrates the results

on the design of multifilter banks and orthonormal multiwavelet bases several forms of parametric expressions for orthogonal multifilter banks are presented the explicit expressions for a group of orthogonal multifilter banks that generate symmetric antisymmetric scaling functions and orthonormal multiwavelets are obtained based on these parametric expressions for orthogonal multifilter banks orthonormal multiwavelet pairs with good time frequency localization are constructed and examples of optimal multifilter banks are provided

h filtering for fuzzy systems with immeasurable premise variables an uncertain system approach this paper discusses a design of stable filters with h disturbance attenuation of takagi sugeno fuzzy systems with immeasurable premise variables when we consider the filter design of takagi sugeno fuzzy systems the selection of premise variables plays an important role if the premise variable is the state of the system then a fuzzy system describes a wide class of nonlinear systems in this case however a filter design of fuzzy systems based on parallel distributed compensator idea is infeasible to avoid such a difficulty we consider the premise variables uncertainties then we consider a robust h filtering problem for such an uncertain system a solution of the problem is given in terms of linear matrix inequalities lmis some numerical examples are given to illustrate our theory

hyperbolic conservation laws with relaxation the effect of relaxation is important in many physical situations it is present in the kinetic theory of gases elasticity with memory gas flow with thermo non equilibrium water waves etc the governing equations often take the form of hyperbolic conservation laws with lower order terms in this article we present and analyze a simple model of hyperbolic conservation laws with relaxation effects dynamic subcharacteristics governing the propagation of disturbances over strong wave forms are identified stability criteria for diffusion waves expansion waves and traveling waves are found and justified nonlinearly time asymptotic expansion and the energy method are used in the analysis for dissipative waves the expansion is similar in spirit to the chapman enskog expansion in the kinetic theory for shock waves however a different approach is needed

nonseparable multidimensional perfect reconstruction filter banks and wavelet bases for r sup n new results on multidimensional filter banks and their connection to multidimensional nonseparable wavelets are presented among the topics discussed are sampling in multiple dimensions multidimensional perfect reconstruction filter banks the two channel case in multiple dimensions the synthesis of multidimensional filter banks and the design of compactly supported wavelets

an approach to fuzzy control of nonlinear systems stability and design issues presents a design methodology for stabilization of a class of nonlinear systems first the authors represent a nonlinear plant with a takagi sugeno fuzzy model then a model based fuzzy controller design utilizing the concept of the so called parallel distributed compensation is employed the main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system the design procedure is conceptually simple and natural moreover the stability analysis and control design problems can be reduced to linear matrix inequality lmi problems therefore they can be solved efficiently in practice by convex programming techniques for lmis the design methodology is illustrated by application to the problem of balancing and swing up of an inverted pendulum on a cart

existence and non existence of global smooth solutions for p system with relaxation abstract in this paper we consider the cauchy problem for p system with relaxation under the assumption that the relaxation time e is sufficiently small we prove the existence of the global smooth solution to the cauchy problem with c1 initial data provided the c0 norm of the derivative of the initial data is of the order of e here is a small positive constant on the other hand when the initial density has compact support but is not identically zero we prove the global regular solution for the cauchy problem does not exist

asymptotic stability of relaxation shock profiles for hyperbolic conservation laws abstract this paper studies the asymptotic stability of traveling relaxation shock profiles for hyperbolic systems of conservation laws under a stability condition of subcharacteristic type the large time relaxation dynamics on the level of shocks is shown to be determined by the equilibrium conservation laws the proof is due to the energy principle using the weighted norms the interaction of waves from various modes is treated by imposing suitable weight matrix

comments on robust stabilization of a class of uncertain nonlinear systems via fuzzy control quadratic stabilizability h sup spl infin control theory and linear matrix inequalities this paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust fuzzy controllers to stabilize the uncertain nonlinear systems first a stability condition for takagi and sugeno s fuzzy model is given in terms of lyapunov stability theory next new stability conditions for a generalized class of uncertain systems are derived from robust control techniques such as quadratic stabilization h sup spl infin control theory and linear matrix inequalities the derived stability conditions are used to analyze the stability of takagi and sugeno s fuzzy control systems with uncertainty which can be regarded as a generalized class of uncertain nonlinear systems the design method employs the so called parallel distributed compensation important issues for the stability analysis and design are remarked finally three design examples of fuzzy controllers for stabilizing nonlinear systems and uncertain nonlinear systems are presented

fuzzy regulators and fuzzy observers relaxed stability conditions and lmi based designs this paper presents new relaxed stability conditions and lmi linear matrix inequality based designs for both continuous and discrete fuzzy control systems they are applied to design problems of fuzzy regulators and fuzzy observers first takagi and sugeno s fuzzy models and some stability results are recalled to design fuzzy regulators and fuzzy observers nonlinear systems are represented by takagi sugeno s ts fuzzy models the concept of parallel distributed compensation is employed to design fuzzy regulators and fuzzy observers from the ts fuzzy models new stability conditions are obtained by relaxing the stability conditions derived in previous papers lmi based design procedures for fuzzy regulators and fuzzy observers are constructed using the parallel distributed compensation and the relaxed stability conditions other lmi s with respect to decay rate and constraints on control input and output are also derived and utilized in the design procedures design examples for nonlinear systems demonstrate the utility of the relaxed stability conditions and the lmi based design procedures

a discrete kinetic approximation of entropy solutions to multidimensional scalar conservation laws abstract we present a new relaxation approximation to scalar conservation laws in several space variables by means of semilinear hyperbolic systems of equations with a finite number of velocities under a suitable multidimensional generalization of the whitham relaxation subcharacteristic condition we show the convergence of the approximated solutions to the unique entropy solution of the equilibrium cauchy problem

multiscale edge detection using a finite element framework for hexagonal pixel based images in recent years the processing of hexagonal pixel based images has been investigated and as a result a number of edge detection algorithms for direct application to such image structures have been developed we build on this paper by presenting a novel and efficient approach to the design of hexagonal image processing operators using linear basis and test functions within the finite element framework development of these scalable first order and laplacian operators using this approach presents a framework both for obtaining large scale neighborhood operators in an efficient manner and for obtaining edge maps at different scales by efficient reuse of the seven point linear operator we evaluate the accuracy of these proposed operators and compare the algorithmic performance using the efficient linear approach with conventional operator convolution for generating edge maps at different scale levels

orthogonal multiwavelets with optimum time frequency resolution a procedure to design orthogonal multiwavelets with good time frequency resolution is introduced formulas to compute the time durations and the frequency bandwidths of scaling functions and multiwavelets are obtained parameter expressions for the matrix coefficients of the multifilter banks that generate symmetric antisymmetric scaling functions and multiwavelets supported in o n are presented for n 2 6 orthogonal multiwavelets with optimum time frequency resolution are constructed and some optimal multifilter banks are provided

a multiple lyapunov function approach to stabilization of fuzzy control systems this paper addresses stability analysis and stabilization for takagi sugeno fuzzy systems via a so called fuzzy lyapunov function which is a multiple lyapunov function the fuzzy lyapunov function is defined by fuzzily blending quadratic lyapunov functions based on the fuzzy lyapunov function approach we give stability conditions for open loop fuzzy systems and stabilization conditions for closed loop fuzzy systems to take full advantage of a fuzzy lyapunov function we propose a new parallel distributed compensation pdc scheme that feedbacks the time derivatives of premise membership functions the new pdc contains the ordinary pdc as a special case a design example illustrates the utility of the fuzzy lyapunov function approach and the new pdc stabilization method

stability analysis of discrete time fuzzy dynamic systems based on piecewise lyapunov functions this paper presents a stability analysis method for discrete time takagi sugeno fuzzy dynamic systems based on a piecewise smooth lyapunov function it is shown that the stability of the fuzzy dynamic system can be established if a piecewise lyapunov function can be constructed and moreover the function can be obtained by solving a set of linear matrix inequalities that is numerically feasible with commercially available software it is also demonstrated via numerical examples that the stability result based on the piecewise quadratic lyapunov functions is less conservative than that based on the common quadratic lyapunov functions

blow up conditions for two dimensional modified euler poisson equations abstract the multi dimensional euler poisson system describes the dynamic behavior of many important physical flows yet as a hyperbolic system its solution can blow up for some initial configurations this article strives to advance our understanding on the critical threshold phenomena through the study of a two dimensional modified euler poisson system with a modified riesz transform where the singularity at the origin is removed we identify upper thresholds for finite time blow up of solutions for the modified euler poisson equations with attractive repulsive forcing

decentralized pdc for large scale t s fuzzy systems this paper studies the decentralized stabilization problem for a large scale system the considered large scale system comprises of a number of subsystems and each subsystem is represented by a takagi sugeno t s fuzzy model the interconnection between any two subsystems may be nonlinear and satisfies some matching condition by the concept of parallel distributed compensation pdc the decentralized fuzzy control for each subsystem is synthesized in which the control gain depends on the strength of interconnections maximal number of the fired rules in each subsystem and the common positive matrix p sub i based on lyapunov criterion and riccati inequality some sufficient conditions are derived and the common p sub i is solved by linear matrix inequalities lmi so that the whole closed loop large scale fuzzy system with the synthesized fuzzy control is asymptotically stable finally a numerical example is given to illustrate the control synthesis and its effectiveness

decentralized h_ infty filter design for discrete time interconnected fuzzy systems this paper describes a decentralized h infin filter design for discrete time interconnected fuzzy systems based on piecewise quadratic lyapunov functions the systems consist of j discrete time interconnected takagi sugeno t s fuzzy subsystems and a decentralized h infin filter is designed for each subsystem it is shown that the stability of the overall filtering error system with h infin performance can be established if a piecewise quadratic lyapunov function can be constructed moreover the parameters of filters can be obtained by solving a set of linear matrix inequalities that are numerically feasible two simulation examples are given to show the effectiveness of the proposed approach