describing function method for stability analysis of pd and pi fuzzy controllers a fuzzy logic controller saturates outside the universe of discourse region this saturation gives rise to a universal nonlinearity for this type of controller in this paper the effects of this nonlinearity are analyzed for the most usual fuzzy controllers pd and pi fuzzy controllers it is shown that due to this saturation some pathological behaviors such as oscillations or unstable limit cycles can occur the methodology employed in the analysis is based on the describing function which is determined for pd and pi fuzzy controllers one example illustrates the relevance of the proposed methodology

homogenization limits and wigner transforms we present a theory for carrying out homogenization limits for quadratic functions called energy densities of solutions of initial value problems ivps with anti self adjoint spatial pseudo differential operators pdos the approach is based on the introduction of phase space wigner matrix measures that are calculated by solving kinetic equations involving the spectral properties of the pdo the weak limits of the energy densities are then obtained by taking moments of the wigner measure the very general theory is illustrated by typical examples like semi classical limits of schrodinger equations with or without a periodic potential the homogenization limit of the acoustic equation in a periodic medium and the classical limit of the dirac equation 1997 john wiley sons inc

output feedback direct adaptive fuzzy controller based on frequency domain methods this paper describes a design method that guarantees the stability of an adaptive fuzzy control system the system consists of an unstable plant with an irrational transfer function a takagi sugeno fuzzy adaptive controller a nonlinear reference model and an adaptation mechanism the gradient based adaptation mechanism changes the consequents of the controller rules in such a way that the closed loop system behaves like the reference model the proposed design procedure utilizes frequency domain methods in the forms of the nyquist and circle criteria it is assumed that the function of the fuzzy controller is a nonlinearity described by a sector condition this condition means that the controller function lies between two lines passing through the origin in this method the function of the fuzzy controller is verified during online adaptation therefore it stays in the allowed sector this method is illustrated by an example of a control system containing an unstable plant with a transport delay the main contribution of this paper is to use frequency methods combined with adaptive fuzzy control these methods have previously been used for nonadaptive fuzzy control but in this paper they are used for the first time for adaptive fuzzy control

bispectrum estimation a parametric approach higher order spectra contain information about random processes that is not contained in the ordinary power spectrum such as the degree of nonlinearity and deviations from normality estimation of the bispectrum which is a third order spectrum has been applied in various fields to obtain information regarding quadratic phase coupling among harmonic components and non gaussianness of processes existing methods of bispectrum estimation are patterned after the conventional methods of power spectrum estimation which are known to possess certain limitations the paper proposes a parametric approach to bispectrum estimation based on a non gaussian white noise driven autoregressive ar model the ar parameter estimates are obtained by solving the third order recursion equations which may be toeplitz in form but not symmetric it is shown that the method provides bispectral estimates that are far superior to the conventional estimates in terms of bispectral fidelity and that in the case of detecting phase coupling among sinusoids the method provides significantly better resolution

identifiability of general arma processes using linear cumulant based estimators abstract cumulants of order greater than two may be used to estimate the parameters of non gaussian arma processes observed in additive colored gaussian noise the arma model may be causal or non causal mixed phase and have inherent all pass factors and repeated poles recent counterexamples to existing algorithms based on third order cumulants have given rise to questions of uniqueness and consistency of the parameter estimates two new order and parameter estimation algorithms are derived and consistency of the estimators is established these algorithms involve the solution of sets of linear equations and may be based on cumulants of any order greater than three it is demonstrated that the counterexamples do not apply to the new methods

a hybrid phase flow method for hamiltonian systems with discontinuous hamiltonians in this paper we propose a new phase flow method for hamiltonian systems with discontinuous hamiltonians in the original phase flow method introduced by ying and candes j comput phys 220 2006 pp 184 215 the phase map should be smooth to ensure the accuracy of the interpolation such an interpolation is inaccurate if the phase map is nonsmooth for example when the hamiltonian is discontinuous we modify the phase flow method using a discontinuous hamiltonian solver and establish the stability for piecewise constant potentials of such a solver this extends the applicability of the highly efficient phase flow method to singular hamiltonian systems with a mild increase of algorithm complexity such a particle method can be useful for the computation of high frequency waves through interfaces

godunov type methods for conservation laws with a flux function discontinuous in space scalar conservation laws with a flux function discontinuous in space are approximated using a godunov type method for which a convergence theorem is proved the case where the flux functions at the interface intersect is emphasized a very simple formula is given for the interface flux a numerical comparison between the godunov numerical flux and the upstream mobility flux is presented for two phase flow in porous media a consequence of the convergence theorem is an existence theorem for the solution of the scalar conservation laws under consideration furthermore for regular solutions uniqueness has been shown

modeling and identification of symmetric noncausal impulse responces spectrally equivalent causal sec models for single input single output noncausal systems are derived with the objective of estimating the noncausal impulse response attention is restricted to symmetric noncausal impulse responses and the measurements of the system output are assumed to be noisy it is shown that by using structured sec models either state space or arma plus noise consistent estimates of the noncausal impulse response can be obtained by exploiting only the second order statistics of the measurements a new version of the correlation technique particularly suited to structured models is presented and analyzed computer simulation results are also presented to illustrate the performance of the proposed approach

quadratic stability analysis of fuzzy model based control systems using staircase membership functions this paper presents the stability analysis of fuzzy model based fmb control systems staircase membership functions are introduced to facilitate the stability analysis through the staircase membership functions approximating those of the fuzzy model and fuzzy controller the information of the membership functions can be brought into the stability analysis based on the lyapunov stability theory stability conditions in terms of linear matrix inequalities lmis are derived in a simple and easy to understand manner to guarantee the system stability the proposed stability analysis approach offers a nice property that includes the membership functions of both fuzzy model and fuzzy controller in the lmi based stability conditions for a dedicated fmb control system furthermore the proposed stability analysis approach can be applied to the fmb control systems of which the membership functions of both fuzzy model and fuzzy controller are not necessarily the same greater design flexibility is allowed to choose the membership functions during the design of fuzzy controllers by employing membership functions with simple structure it is possible to lower the structural complexity and the implementation cost simulation examples are given to illustrate the merits of the proposed approach

stability of a resonant system of conservation laws modeling polymer flow with gravitation abstract we prove l 1 uniqueness and stability for a resonant 2 2 system of conservation laws that arise as a model for two phase polymer flow in porous media the analysis uses the equivalence of the eulerian and lagrangian formulation of this system and the results are first established for an auxiliary scalar equation our methods are based on front tracking approximations for the auxiliary equation and the kru kov entropy condition for scalar conservation laws

convergence of a difference scheme for conservation laws with a discontinuous flux convergence is established for a scalar finite difference scheme based on the godunov or engquist osher eo flux for scalar conservation laws having a flux that is spatially dependent through a possibly discontinuous coefficient other works in this direction have established convergence for methods employing the solution of 2 2 riemann problems the algorithm discussed here uses only scalar riemann solvers satisfaction of a set of kruzkov type entropy inequalities is established for the limit solution from which geometric entropy conditions follow assuming a piecewise constant coefficient it is shown that these conditions imply l1 contractiveness for piecewise c1 solutions thus extending a well known theorem

identification of linear stochastic systems via second and fourth order cumulant matching the identification problem for time invariant single input single output linear stochastic systems driven by non gaussian white noise is considered the system is not restricted to be minimum phase and it is allowed to contain all pass components a least squares criterion that involves matching the second and the fourth order cumulant functions of the noisy observations is proposed knowledge of the probability distribution of the driving noise is not required an order determination criterion that is a modification of the akaike information criterion is also proposed strong consistency of the proposed estimator is proved under certain sufficient conditions simulation results are presented to illustrate the method

a hybrid phase flow method for solving the liouville equation in a bounded domain the phase flow method originally introduced in l x ying and e j candes j comput phys 220 2006 pp 184 215 can efficiently solve autonomous ordinary differential equations in s jin h wu and z y huang siam j sci comput 31 2008 pp 1303 1321 the method was generalized to solve hamiltonian system where the hamiltonian function was discontinuous however both of these methods require a phase flow map constructed on an invariant manifold this can increase computational cost when the invariant domain is big or unbounded following the idea of s jin h wu and z y huang siam j sci comput 31 2008 pp 1303 1321 we propose a hybrid phase flow method for solving the liouville equation in a bounded domain which is smaller than the invariant manifold of a phase flow map by using some proper boundary conditions this method can help solve the problem where the invariant manifold of a phase flow map determined by the liouville equation is unbounded we verify numerical accuracy and efficiency by several examples of the semiclassical limit of the schrodinger equation analysis of numerical stability and convergence is given for the semiclassical limit equation with inflow boundary condition

deconvolution and estimation of transfer function phase and coefficients for nongaussian linear processes nongaussian linear processes are considered it is shown that the phase of the transfer function can be estimated under broad conditions this is not true of gaussian linear processes and in this sense gaussian linear processes are atypical the asymptotic behavior of a phase estimate is determined the phase estimates make use of bispectral estimates these ideas are applied to a problem of deconvolution which is effective even when the transfer function is not minimum phase a number of computational illustrations are given

stability analysis of polynomial fuzzy model based control systems using switching polynomial lyapunov function this paper investigates the stability problem of polynomial fuzzy model based control system which is formed by a polynomial fuzzy model and a polynomial fuzzy controller connected in a closed loop a switching polynomial lyapunov function consisting of a number of local polynomial lyapunov functions is proposed to investigate the system stability it demonstrates a nice property in favor of the stability analysis that each local polynomial lyapunov function transits continuously to each other as different local polynomial lyapunov functions are employed to investigate the system stability according to the operating domain relaxed stability conditions compared with the stability analysis result with a common lyapunov function can be developed in order to allow a greater design flexibility for the polynomial fuzzy controller the proposed polynomial fuzzy model based control scheme does not require that both the polynomial fuzzy model and polynomial fuzzy controller share the same premise membership functions stability conditions in terms of sum of squares are obtained to guarantee system stability and facilitate control synthesis simulation examples are given to verify the stability analysis results and demonstrate the effectiveness of the proposed polynomial fuzzy control scheme

fitting noncausal autoregressive signal plus noise models to noisy non gaussian linear processes the problem of estimating the parameters of a noncausal autoregressive signal model from noisy observations is considered the signal is assumed to be non gaussian the measurement noise is allowed to be non gaussian two techniques that use both autocorrelations and third order autocumulants of the data are presented for parameter estimation knowledge of the probability distribution of the driving noise is not required several simulation examples are presented to illustrate the two methods the problem of model order selection is also addressed

identification of non minimum phase linear stochastic systems abstract the identification of time invariant non minimum phase stochastic systems driven by non gaussian white noise is considered given only the noisy observations of the system output a two step procedure is proposed in the first step a spectrally equivalent system is estimated using a standard technique that exploits only the second order statistics of the measurements in the second step a partial set of 4th order cumulants of the measurements is exploited to resolve the location of the system zeros knowledge of the probability distribution of the driving noise is not required strong consistency of the proposed estimator is proved under certain sufficient conditions simulation results are also presented in support of the theory

typical takagi sugeno pi and pd fuzzy controllers analytical structures and stability analysis in the first part of this paper we investigate explicit structure of the typical takagi sugeno ts fuzzy pi and pd controllers by typical we mean the use of at least three trapezoidal or triangular input fuzzy sets for each input variable fuzzy rules with linear consequent zadeh fuzzy logic and operator and the centroid defuzzifier this configuration covers many ts fuzzy controllers in the literature we mathematically prove these fuzzy controllers to be nonlinear pi or pd controllers with proportional gain and integral gain or derivative gain changing with output of the controlled system we reveal these fuzzy controllers to be inherently nonlinear gain scheduling pi or pd controllers with different variable gains in different regions of input space the gains constantly change even in the same region and switch continuously and smoothly between adjacent regions the explicit structural expressions of the fuzzy controllers are derived and their characteristics including the bounds and geometrical shape of the gain variation are studied in the second part of the paper we apply the small gain theorem to the derived structures of the fuzzy controllers and establish a sufficient global bibo stability criterion for nonlinear systems controlled by the fuzzy controllers local stability is also examined

higher order spectrum estimation via noncausal autoregressive modeling and deconvolution a method for nonminimum phase finite impulse response fir system identification is introduced that is based on noncausal autoregressive ar modeling of the third moments of the output data the magnitude and phase response of the fir system are expressed in terms of the parameters of a noncausal ar model the set of ar parameters is obtained by solving an overdetermined linear system of equations that is formed using third moment estimates of the output data the performance of the method is illustrated with simulation examples

a unifying maximum likelihood view of cumulant and polyspectral measures for non gaussian signal classification and estimation classification and estimation of non gaussian signals observed in additive gaussian noise of unknown covariance are addressed using cumulants or polyspectra by integrating ideas from pattern recognition and model identification asymptotically optimum maximum likelihood classifiers and arma autoregressive moving average parameter estimators are derived without knowledge of the data distribution identifiability of noncausal and nonminimum phase arma models is established using a finite number of cumulant or polyspectral lags of any order greater than two a unifying view of cumulant and polyspectral discriminant measures utilizes these lags and provides a common framework for development and performance analysis of novel and existing estimation and classification algorithms tentative order determination and model validation tests for non gaussian arma processes are described briefly illustrative simulations are also presented

computing multivalued physical observables for the semiclassical limit of the schrodinger equation we develop a level set method for the computation of multivalued physical observables density velocity etc for the semiclassical limit of the schrodinger equation this method uses an eulerian formulation and applies directly to arbitrary number of space dimensions the main idea is to evolve the density near an n dimensional manifold that is identified as the common zeros of n level set functions in phase space these level set functions are generated from solving the liouville equation with initial data chosen to embed the phase gradient simultaneously we track a new quantity f by solving again the liouville equation near the obtained zero level set but with initial density as initial data the multivalued density and higher moments are thus resolved by integrating f along the n dimensional manifold in the phase directions we show that this is equivalent to using the wigner approach but decomposing the velocity from the density each of which evolves by the same liouville equation the main advantages of this approach in contrast to the standard kinetic equation approach using the liouville equation with a dirac measure initial data include 1 the liouville equations are solved with l initial data and a singular integral involving the email protected function is evaluated only in the post processing step thus avoiding oscillations and excessive numerical smearing 2 a local level set method can be utilized to significantly reduce the computation in the phase space these advantages allow us to compute for the first time all physical observables for multidimensional problems in an eulerian framework

order reduction of siso nonminimum phase stochastic systems we consider the order reduction problem for single input single output nonminimum phase linear stochastic systems the problem is formulated as that of approximating the original system output process by another stochastic process generated via a reduced order model it is shown that in order to obtain a correct phase approximation it is necessary to consider some higher order statistics of the original process in addition to the usual second order statistics a computationally feasible approximation criterion is proposed and analyzed an example is also presented to illustrate the proposed method

a difference scheme for conservation laws with a discontinuous flux the nonconvex case in a previous work by the author convergence was established for a simple difference scheme approximating a scalar conservation law where the flux was concave and had a discontinuous spatially varying coefficient j d towers siam j numer anal 38 2000 pp 681 698 the main result of this paper is an extension of that convergence theorem to the situation where the flux may have any finite number of critical points additionally spatially varying source terms are allowed the spatially varying numerical flux is also shown to satisfy maximum and minimum principles and to be total variation decreasing tvd in time

new results on delay dependent robust stability criteria of uncertain fuzzy systems with state and input delays this paper focuses on the delay dependent stability analysis and stabilization for uncertain t s fuzzy control systems with state and input delays the key features of the approach include the introduction of uncorrelated augmented matrix items into the lyapunov functional and the use of a tighter bounding technology in fact these techniques lead to more general and less conservative stability conditions that guarantee a wide stability region our delay dependent stability conditions thus obtained are given in terms of linear matrix inequalities lmis finally some examples are included to show that the proposed criteria improve the existing results significantly

stability analysis of the simplest takagi sugeno fuzzy control system using circle criterion in this paper we present two sufficient conditions in the frequency domain for the global stability analysis of the simplest takagi sugeno t s fuzzy control system based on the circle criterion and its graphical interpretation these conditions are significant in graphically designing the simplest t s fuzzy controller in the frequency domain four numerical examples are provided to demonstrate the efficiency of our two frequency domain based conditions furthermore this t s fuzzy controller and the linear proportional controllers are also compared it is concluded that the simplest t s fuzzy controller can outperform the linear proportional controllers in a noisy environment with external disturbances

a robust multi objective dpdc for uncertain t s fuzzy systems this paper offers a design procedure for a robust pole placement problem with h objective via dynamic output feedback control for a class of uncertain fuzzy systems takagi sugeno t s fuzzy system is used for modeling and dynamic parallel distributed compensation dpdc technique is employed in the controller design solutions to the problems are derived in terms of a family of linear matrix inequalities lmis and uncertainties are directly considered in the conditions that determine the controller effectiveness of the proposed design technique is illustrated by simulation for an inverted pendulum system

limit cycle prediction of a fuzzy control system based on describing function method a limit cycle is the phenomenon that can be observed in systems composed of nonlinear elements the phenomenon is of fundamental importance in nonlinear systems and as far as the design of a nonlinear system is concerned it should be considered along with the stability analysis in the paper the limit cycle of a system controlled by a fuzzy logic controller flc is addressed via some of the classical control techniques used to analyze nonlinear systems in the frequency domain first reasonable assumptions are made on the structure of the flc by using fuzzy basis functions fbfs and the describing function of the flc is derived to analyze and predict the existence of the limit cycle of the closed loop system including the flc finally computer simulation is performed to show how the analysis given in the paper is used to predict the existence of the limit cycle of the fuzzy control system

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

lmi based robust stability analysis for fuzzy feedback linearization regulators with its applications in order to cope with parametric uncertainties of nonlinear systems a numerical analysis method of a robust feedback linearization control scheme based on fuzzy models is proposed the fuzzy feedback linearization control scheme ensures that the control operates stably under bounded parametric uncertainties for the system with known uncertainty bounds linear matrix inequality based robust stability condition is derived and a robust fuzzy feedback linearization regulators can be designed by choosing the control parameters satisfying the inequalities which give sufficient conditions for the closed loop system to be stable to verify the validity and effectiveness of the designed stability analysis methods the suggested analysis techniques are applied to a balancing control of inverted pendulum systems

ordinary differential equations transport theory and sobolev spaces we obtain some new existence uniqueness and stability results for ordinary differential equations with coefficients in sobolev spaces these results are deduced from corresponding results on linear transport equations which are analyzed by the method of renormalized solutions

parameter estimation for noncausal arma models of non gaussian signals via cumulant matching we consider the problem of estimating the parameters of a stable stationary scalar arma p q signal model driven by an i i d non gaussian sequence the driving noise sequence is not observed the signal is allowed to be nonminimum phase and or noncausal i e poles may lie both inside as well as outside the unit circle we address the problem of parameter identifiability given the higher order cumulants of the signal on a finite set of lags the sufficient set of lags required to achieve parameter identifiability is the smallest to date the sufficient conditions for parameter identifiability are also the least restrictive to date we also propose a frequency domain approach for time domain nonlinear optimization of a quadratic cumulant matching criterion illustrative computer simulation results are presented

robust h control for discrete time fuzzy systems via basis dependent lyapunov functions this paper deals with the robust h control problem for a class of discrete time fuzzy systems with uncertainty the uncertainty is assumed to be of structured linear fractional form by using basis dependent lyapunov function an h control design approach is developed the control design approach is facilitated by introducing some additional instrumental matrix variables these additional matrix variables decouple the lyapunov and the system matrices which makes the control design feasible the proposed approach leads to some sufficient results in the form of strict linear matrix inequalities lmis it is expected that the basis dependent results are less conservative than the basis independent ones due to the introduction of basis dependent lyapunov function finally numerical examples including the discrete chaotic lorenz system are also given to demonstrate the applicability of the proposed approach

graphical l2 stability analysis of takagi sugeno control systems in the frequency domain in this paper the upper bound of the l2 gain of the continuous time siso takagi sugeno t s fuzzy system is first graphically obtained in the frequency domain based on this upper bound of the l2 gain the l2 stability of the above t s fuzzy control system is next investigated by using the small gain theorem and circle criterion two sufficient conditions are derived which can be employed to graphically investigate the l2 stability of certain kind of t s fuzzy control system in the frequency domain one numerical example is presented to illustrate how the l2 stability of the simplified continuous time t s fuzzy system can be graphically examined

feedback control of nonlinear systems by extended linearization for single input multiple output nonlinear systems we consider a design method based on the family of linearizations of the system parameterized by constant operating points nonlinear state feedback control laws and observer state feedback control laws are designed such that the eigenvalues of the family of linearized closed loop systems are placed at specified values that are locally invariant with respect to the closed loop operating point the method is illustrated by application to the problem of automatically balancing an inverted pendulum

multichannel arma processes parametric modeling of multichannel time series is accomplished by using higher than second order statistics hos of the observed nongaussian data cumulants of vector processes are defined using a kronecker product formulation and consistency of their sample estimators is addressed identifiability results in connection with the hos based parameter estimation of causal and noncausal multivariate arma processes are established estimates of the parameters of causal arma models are obtained as the solution to a set of linear equations whereas those of noncausal arma models are obtained as the solution to a cumulant matching algorithm conventional approaches based on second order statistics can identify a multichannel system only to within post multiplication by a unimodular matrix hos based methods yield solutions that are unique to within post multiplication by an extended permutation matrix additionally the multiminimum phase assumption can be relaxed and the observations may be contaminated with colored gaussian noise frequency domain methods for nonparametric system identification are discussed briefly simulations results validating the multichannel parameter estimation algorithms are provided

stability analysis of fuzzy control systems in this paper we present a general review of the stability issue as related to fuzzy control systems the concept of stability and the general criterion used for fuzzy control systems are discussed the intuitive and nonlinear system stability analysis of fuzzy control systems are given popov s technique is proposed to test the stability of fuzzy systems

stability analysis of nonlinear multivariable takagi sugeno fuzzy control systems points out how the nonlinearities involved in multivariable takagi sugeno t s fuzzy control systems could originate complex behavior phenomena such as multiple equilibrium points or limit cycles that cannot be detected using conventional stability analysis techniques in the paper the application of mimo frequency domain methods to predict the existence of multiple equilibria and of limit cycles are presented the proposed method is based on the formulation of a lur e problem from the original structure of a t s fuzzy system with a fuzzy controller furthermore this technique makes straightforward the application of input output stability techniques such as the multivariable circle criterion also called the conicity criterion and the harmonic balance method moreover in the paper the application of the harmonic balance method has been generalized to the case of a mimo fuzzy system with asymmetric nonlinearities and improved by the decreasing conservatism a new and more general stability index which could be used to perform a bifurcation analysis of fuzzy control systems is presented the paper includes a collection of examples where the advantages of the proposed approach are made explicit comparing it to the input output conicity criterion and the lyapunov direct method

numerical approximations of one dimensional linear conservation equations with discontinuous coefficients conservative linear equations arise in many areas of application including continuum mechanics or high frequency geometrical optics approximations this kind of equations admits most of the time solutions which are only bounded measures in the space variable known as duality solutions in this paper we study the convergence of a class of finite differences numerical schemes and introduce an appropriate concept of consistency with the continuous problem some basic examples including computational results are also supplied

consistent parameter estimation for non causal autoregressive model via higher order statistics abstract the problem of estimating the parameters of a non causal autoregressive ar model given the noisy observations of the system output is considered the system is driven by an i i d independent and identically distributed non gaussian sequence that is not observed the measurement noise is additive i i d and possibly non gaussian a parameter estimator that involves simultaneous matching of data autocorrelations and third order auto cumulants was recently proposed for the estimation of the parameters of non causal ar models in the proposed method the maximum cumulant lag used in cumulant matching was specified as large but finite in this paper we give a specific lower bound to the maximum cumulant lag and we prove the strong consistency of the parameter estimator under the specified choice of lags some recently developed fundamental results concerning the recovery of the poles of a causal system from the third order statistics of the system output play a crucial role in this paper

output feedback lmi tracking control conditions with h criterion for uncertain and disturbed t s models this work concerns the tracking problem of uncertain takagi sugeno t s continuous fuzzy model with external disturbances the objective is to get a model reference based output feedback tracking control law the control scheme is based on a pdc structure a fuzzy observer and a h performance to attenuate the external disturbances the stability of the whole closed loop model is investigated using the well known quadratic lyapunov function the key point of the proposed approaches is to achieve conditions under a lmi linear matrix inequalities formulation in the case of an uncertain and disturbed t s fuzzy model this formulation facilitates obtaining solutions through interior point optimization methods for some nonlinear output tracking control problems finally a simulation is provided on the well known inverted pendulum testbed to show the efficiency of the proposed approach

the l 1 error estimates for a hamiltonian preserving scheme for the liouville equation with piecewise constant potentials we study the l 1 error of a hamiltonian preserving scheme developed in s jin and x wen commun math sci 3 2005 pp 285 315 for the liouville equation with a piecewise constant potential in one space dimension this problem has important applications in computations of the semiclassical limit of the linear schrodinger equation through barriers and of the high frequency waves through interfaces we use the l 1 error estimates established in x wen and s jin j comput math 26 2008 pp 1 22 x wen convergence of an immersed interface upwind scheme for linear advection equations with piecewise constant coefficients ii some related binomial coefficient inequalities preprint 2008 for the immersed interface upwind scheme to the linear advection equations with piecewise constant coefficients we prove that the scheme with the dirichlet incoming boundary conditions is l 1 convergent for a class of bounded initial data and derive the half order l 1 error bounds with explicit coefficients the initial conditions can be satisfied by applying the decomposition technique proposed in s jin h l liu s osher and r tsai j comput phys 205 2005 pp 222 241 for solving the liouville equation with measure valued initial data which arises in the semiclassical limit of the linear schrodinger equation

viscosity solutions and convergence of monotone schemes for synthetic aperture radar shape from shading equations with discontinuous intensities the shape from shading sfs equation relating u y r the unknown angular height of a surface to i y r the known synthetic aperture radar sar intensity data from the surface is i frac u r 2 sqrt 1 u r 2 u y 2 where y and r are axial and radial cylindrical coordinates unlike the more common eikonal sfs equation which relates surface height in cartesian coordinates to optical photographic intensity data the above radar equation can be transformed into hamilton jacobi cauchy form ur g i uy 0 we explore the case where i is a discontinuous function which occurs commonly in radar data by considering sequences of continuous intensity functions that converge to i we obtain corresponding sequences of viscosity solutions we prove that these sequences must converge we also establish conditions that guarantee that these sequences converge to a common limit which we define as the solution to the radar equation finally we establish and demonstrate that when this common limit exists monot

on estimating noncausal nonminimum phase arma models of non gaussian processes the authors address the problem of estimating the parameters of non gaussian arma autoregressive moving average processes using only the cumulants of the noisy observation the measurement noise is allowed to be colored gaussian or independent and identically non gaussian distributed the arma model is not restricted to be causal or minimum phase and may even contain all pass factors the unique parameter estimates of both the ma and ar parts are obtained by linear equations the structure of the proposed algorithm facilitates asymptotic performance evaluation of the parameter estimators and model order selection using cumulant statistics the method is computationally simple and can be viewed as the least squares solution to a quadratic model fitting of a sampled cumulant sequence identifiability issues are addressed simulations are presented to illustrate the proposed algorithm

noncausal nonminimum phase arma modeling of non gaussian processes a method is presented for the estimation of the parameters of a noncausal nonminimum phase arma model for non gaussian random processes using certain higher order cepstra slices the fourier phases of two intermediate sequences h sub min n and h sub max n can be computed where h sub min n is composed of the minimum phase parts of the ar and ma models and h sub max n of the corresponding maximum phase parts under the condition that there are no zero pole cancellations in the arma model these two sequences can be estimated from their phases only and lead to the reconstruction of the ar and ma parameters within a scalar and a time shift the ar and ma orders do not have to be estimated separately but they are by product of the parameter estimation procedure through simulations it is shown that unlike existing methods the estimation procedure is fairly robust if a small order mismatch occurs since the robustness of the method in the presence of additive noise depends on the accuracy of the estimated phases of h sub min n and h sub max n the phase errors due to finite length data are studied and their statistics are derived

stochastic system identification with noisy input using cumulant statistics addresses the problem of estimating the parameters of stochastic linear systems when the measurements of the system input as well as the system output are noise contaminated it is assumed that the input is non gaussian and the noises are gaussian the square root of the magnitude of the fourth cumulant of a generalized error signal is proposed as a performance criterion for parameter estimation an optimization algorithm is presented strong consistency of the proposed parameter estimators is proved under certain sufficient conditions both single input single output and multiple input multiple output cases are investigated finally simulation results are presented to illustrate the proposed approach

a comparison of convergence rates for godunov s method and glimm s method in resonant nonlinear systems of conservation laws we obtain time independent bounds on derivatives prove convergence and establish a rate of convergence for godunov s numerical method as applied to the initial value problem for a resonant inhomogeneous conservation law which is treated as a 2 times 2 nonstrictly hyperbolic system we compare the results with a corresponding analysis of glimm s method and see that our analysis gives equivalent sharp convergence rates in the strictly hyperbolic setting but an improvement is seen in godunov s method over glimm s method in the nonstrictly hyperbolic resonant regime the 2 times 2 glimm and godunov methods are the only methods for which we can obtain time independent bounds on derivatives these bounds represent a purely nonlinear phenomenon because there are no corresponding time independent bounds for the linearized equations which blow up at a linear rate in time

piecewise quadratic stability of fuzzy systems presents an approach to stability analysis of fuzzy systems the analysis is based on lyapunov functions that are continuous and piecewise quadratic the approach exploits the gain scheduling nature of fuzzy systems and results in stability conditions that can be verified via convex optimization over linear matrix inequalities examples demonstrate the many improvements over analysis based on a single quadratic lyapunov function special attention is given to the computational aspects of the approach and several methods to improve the computational efficiency are described

design of state feedback adaptive fuzzy controllers for second order systems using a frequency stability criterion this paper proposes a design method for second order systems that guarantees the stability of an adaptive fuzzy controller with state feedback the system consists of a linear unstable plant the takagi sugeno controller a nonlinear reference model and an adaptation mechanism in this paper gradient based adaptation is used to change the consequents of the controller rules so that the closed loop system behaves like the reference model the proposed method utilizes a frequency domain criterion in the form of the modified circle theorem the controller function is assumed to be a nonlinearity described by a sector condition which means that the function lies between two planes during the process of adaptation this function is verified so it stays in the sector guaranteeing stability the method described here is illustrated by an example of a control system containing an unstable plant with an unknown pole in the right half plane the motivation of this paper is to propose a frequency domain method for the design of state feedback adaptive fuzzy controllers comparing with time domain methods that require advanced software tools the proposed method offers simple graphical interpretation on the nyquist plane