orthogonalization process by recurrence relations an orthogonalization process is proposed applicable to spaces which are realizations of abstract hilbert space it is simpler than the gram schmidt process a recurrence relation which orthogonalizes a physical space is proposed and it is shown that the generalized langevin equation is contained therein this process serves as a basis for understanding the nature of the dynamic many body formalism

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

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

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

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

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

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

analytical results for long time behavior in anomalous diffusion we investigate through a generalized langevin formalism the phenomenon of anomalous diffusion for asymptotic times and we generalized the concept of the diffusion exponent a method is proposed to obtain the diffusion coefficient analytically through the introduction of a time scaling factor ensuremath lambda we obtain as well an exact expression for ensuremath lambda for all kinds of diffusion moreover we show that ensuremath lambda is a universal parameter determined by the diffusion exponent the results are then compared with numerical calculations and very good agreement is observed the method is general and may be applied to many types of stochastic problem

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

why does boltzmann s ergodic hypothesis work and when does it fail abstract according to a recently given ergodic condition for hermitian many body models the thermodynamic limit and irreversibility are necessary but by themselves not sufficient the sufficient condition turns out to be the existence of a zero frequency mode it is measured by an infinite product of the recurrants from the recurrence relations method which solves the heisenberg equation of motion in hermitian models this condition has been tested with a variety of assemblies of nearest neighbor coupled harmonic oscillators the results provide a physical insight into why the ergodic hypothesis is valid and when it fails

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

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

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

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

fluctuation dissipation dispersion relation and quality factor for slow processes a generalization of the callen welton formula for systems with slowly varying parameters is given using the momentum method and the time multiscale technique it is shown that not only the dissipation but also the dispersive contributions determine the spectral function of the fluctuations in these systems the general formalism is illustrated for an oscillating electrical circuit and the influence of the dispersion contributions on the quality factor of the system is discussed

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

singular solutions for semilinear hyperbolic equations i on construit des solutions avec singularites de type choc pour des equations semilineaires strictement hyperboliques

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

derivation of the generalized langevin equation by a method of recurrence relations the generalized langevin equation was first derived by mori using the gram schmidt orthogonalization process this equation can also be derived by a method of recurrence relations for a physical space commonly used in statistical mechanics the recurrence relations are simple and they lead directly to the langevin equation the langevin equation is shown to be composed of one homogeneous and one inhomogeneous equation

continued fraction matrix representation of response functions in multicomponent systems the continued fraction representation of response functions is developed for a set of dynamical variables various approximation schemes are possible in which the frequency moment sum rules appear explicitly this formalism is applied to light scattering in two component strongly coupled plasmas as an illustrative example

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

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

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

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

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

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

ergodicity in simple and not so simple systems and kubo s condition abstract the ergodic hypothesis is approached from the side of time averaging to ascertain regions of its validity a necessary and sufficient condition is formulated in terms of certain infinite products and tested in models of nn coupled harmonic oscillators the validity of the hypothesis requires energy delocalizability indicated by the existence of coherent translation modes kubo s condition is re examined to see the origin of its limitations

why irreversibility is not a sufficient condition for ergodicity khinchin s theorem of ergodicity is examined by means of linear response theory the resulting ergodic condition shows that contrary to the theorem irreversibility is not a sufficient condition for ergodicity by the recurrence relations method we prove that irreversibility is broader in scope than ergodicity showing why it can only be a necessary condition for ergodicity

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

self spreading and strength of singularities for solutions to semilinear wave equations algebres microlocales propagation de la regularite solutions lineaires conduisant a l etalement auto etalement des singularites

ergodic theory infinite products and long time behavior in hermitian models ergodic theory has been approached from the side of the time averages with correlation functions from many body models the condition for ergodic behavior is formulated in terms of infinite products of certain numbers associated with time evolution physical properties that make a model ergodic are identified

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

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

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

testing boltzmann s ergodic hypothesis with electron gas models kubo proposed a physical approach to proving the validity of boltzmann s ergodic hypothesis it is to perform the time averages on dynamical functions thereby avoiding the difficulties of measure theory inherent in the classical approach to perform time averaging properly one must have a general solution for the heisenberg equation of motion such as by the recurrence relations method a time averaging carried over with a recurrence relations solution is found to yield an ergodic condition in the form of an infinite product it is linked to the energy transfer mechanisms hence to the ergodicity itself the electron gas models are fertile ground for testing ergodicity by this approach for several static domains we have evaluated the infinite product and drawn from them a general physical picture that underlies the ergodic hypothesis

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