extension of noncommutative soliton hierarchies a linear system which generates a moyal deformed two dimensional soliton equation as an integrability condition can be extended to a three dimensional linear system treating the deformation parameter as an additional coordinate the supplementary integrability conditions result in a first order differential equation with respect to the deformation parameter the flow of which commutes with the flow of the deformed soliton equation in this way a deformed soliton hierarchy can be extended to a bigger hierarchy by including the corresponding deformation equations we prove the extended hierarchy properties for the deformed akns hierarchy and specialize to the cases of deformed nls kdv and mkdv hierarchies corresponding results are also obtained for the deformed kp hierarchy a deformation equation determines a kind of seiberg witten map from classical solutions to solutions of the respective noncommutative deformed equation

robust static output feedback stabilization for nonlinear discrete time systems with time delay via fuzzy control approach this paper addresses the problem of designing robust static output feedback controllers for nonlinear discrete time interval systems with time delays both in states and in control input in the approach we do not directly employ the lyapunov approach as do in most of traditional fuzzy control design approaches instead sufficient conditions for guaranteeing the robust stability for the considered systems are derived in terms of the matrix spectral norm of the closed loop fuzzy system the stability conditions are further formulated into linear matrix inequalities so that the desired controller can be easily obtained by using the matlab linear matrix inequality lmi toolbox finally an example is provided to illustrate the effectiveness of the proposed approach

dynamic parallel distributed compensation for takagi sugeno fuzzy systems an lmi approach abstract this paper presents a unified systematic framework for designing dynamic feedback controllers for nonlinear systems described by takagi sugeno t s models both stabilization and multi objective control synthesis problems have been addressed the control laws are in the form of so called dynamic parallel distributed compensation dpdc which are essentially nonlinear dynamic feedback controllers the associated control synthesis problems are formulated as linear matrix inequality lmi problems i e the parameters of the dpdc controllers are obtained from a set of lmi conditions the approach in this paper can also be applied to hybrid or switching systems

improved l2 gain performance controller synthesis for takagi sugeno fuzzy system in this paper an improved l2 gain performance controller synthesis is proposed for takagi sugeno t s fuzzy system the t s fuzzy controller can be easily derived by a three step procedure with the linear matrix inequalities lmis technique first a new t s fuzzy model structure is presented which includes the original t s fuzzy plant with stable pre and post filters on the input and output of the original plant second by using this structure the l2 gain performance controller design problem can be easily transformed into standard lmis formulation compared with the previous results it not only gives us a simple structure of the t s fuzzy controller but also provides us effective lmis based conditions which include a small number of unknown matrix variables consequently less value of l2 gain performance of the closed loop system can be obtained third an augmented t s fuzzy controller which guarantees l2 gain performance is obtained for the original t s fuzzy plant which is composed of the t s controller derived from step two and two stable pre and post filters finally some numerical examples are demonstrated to show the effectiveness of the proposals

multiobjective output feedback control via lmi optimization this paper presents an overview of a linear matrix inequality lmi approach to the multiobjective synthesis of linear output feedback controllers the design objectives can be a mix of h sub spl infin performance h sub 2 performance passivity asymptotic disturbance rejection time domain constraints and constraints on the closed loop pole location in addition these objectives can be specified on different channels of the closed loop system when all objectives are formulated in terms of a common lyapunov function controller design amounts to solving a system of linear matrix inequalities the validity of this approach is illustrated by a realistic design example

characterization of jacobian varieties in terms of soliton equations pour dans le demi espace superieur de siegel h g soit x c g z g z g la variete abelienne principalement polarisee correspondante et soit z z m e z gexp 2 i t mz i t m m la fonction theta de riemann pour x les deux conditions a et b pour x sont equivalentes a 1 il existe des vecteurs a 1 a 2 a 3 c g a 1 0 et une forme quadratique q t i j 1 3 q ij t i t j q ij c tel que pour c g t t exp q t t 1 a 1 t 2 a 2 t 3 a 3 donne une solution a l equation de kadomtsev petviashvili sous la forme d hirota d 1 4 3d 2 2 4d 1 d 3 0 2 le diviseur de x est irreductible b x est isomorphe a la variete jacobienne d une courbe lisse complete de genre g sur c

dynamic output feedback h control synthesis for discrete time t s fuzzy systems via switching fuzzy controllers this paper studies the problem of dynamic output feedback h control of discrete time takagi sugeno t s fuzzy systems via a switched dynamic parallel distributed compensation dpdc scheme the considered switched dpdc control structure is determined based on the values of membership functions some new properties of membership functions are obtained and exploited to derive sufficient conditions for designing switching dpdc controllers that guarantee the stability and h performances of closed loop nonlinear systems the design conditions are given in terms of solvability of a set of linear matrix inequalities lmis it is shown that the new approach provides results at least as good as the corresponding dpdc methods a numerical example is given to illustrate the effectiveness of the proposed approach

robust h control of multiple time delay uncertain nonlinear system using fuzzy model and adaptive neural network in this paper a robust control method which combines fuzzy model based control with adaptive neural network control is presented for a class of uncertain nonlinear system with multiple time delay the fuzzy t s model with multiple time delay is adopted for the approximate modeling of the nonlinear system with some unknown uncertainties and fuzzy model based h control law is designed by means of lmi method a full adaptive rbf neural network is added to the fuzzy h control in order to guarantee the robust stability of the controlled system the effect of the unknown uncertainties and the error caused by fuzzy modeling can be overcome by adaptive tuning of the weights centers and widths of the rbf neural network on line and no constraint or matching conditions are required the stability of the designed closed loop system is thus proved the proposed method is applied to a multiple time delay nonlinear chaotic system and the simulation results show that the proposed method cannot only stabilize the chaos systems but has strong robustness against uncertainties and external disturbance

static output feedback stabilization for nonlinear interval time delay systems via fuzzy control approach abstract this paper addresses the design problem of static output feedback controllers for nonlinear interval time delay systems represented by the takagi sugeno fuzzy model departing from traditional approaches which are to find a common positive definite matrix for all rules sufficient conditions to guarantee the robust stability for such fuzzy systems are derived in term of matrix measures of system matrices in the consequent parts of fuzzy rules these conditions are further transformed into linear matrix inequalities by solving linear matrix inequalities a static output feedback controller that can stabilize the considered uncertain time delay system can easily be obtained finally an example is provided to illustrate the effectiveness of our approach

output feedback fault tolerant control by a set theoretic description of ts fuzzy systems this paper is concerned with the observer based output feedback fault tolerant control problem for ts fuzzy systems by constructing a set theoretic description of fuzzy systems the equivalence class theory in set theory is applied for designing observer and controller for less conservative results firstly we designed the observer to get the information of the actuator faults in the system then we use this information to design the fault tolerant controller to compensate for the effect of faults and guarantee stability of the system finally a simple nonlinear massspringdamper system is presented to illustrate the effectiveness of the proposed approach

static output feedback controller design for fuzzy systems an ilmi approach this paper examines the problem of static output feedback control of a takagi sugeno ts fuzzy system the existence of a static output feedback control law is given in terms of the solvability of bilinear matrix inequalities an iterative algorithm based on the linear matrix inequality is proposed to compute the static output feedback gain to reduce the conservatism of the design the structural information of the membership function of the fuzzy rules is incorporated numerical examples are used to illustrate the validity of the methods

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

l sub 2 gain analysis of nonlinear systems and nonlinear state feedback h sub infinity control previously obtained results on l2 gain analysis of smooth nonlinear systems are unified and extended using an approach based on hamilton jacobi equations and inequalities and their relation to invariant manifolds of an associated hamiltonian vector field on the basis of these results a nonlinear analog is obtained of the simplest part of a state space approach to linear h sub infinity control namely the state feedback h sub infinity optimal control problem furthermore the relation with h sub infinity control of the linearized system is dealt with

robust h_ infty fuzzy control approach for a class of markovian jump nonlinear systems this paper addresses the problem of stabilizing a class of nonlinear systems subject to markovian jump parameters using a robust stochastic fuzzy controller with hinfin performance the class of jump nonlinear systems considered is described by a fuzzy model composed of two levels a crisp level which represents the jumps and a fuzzy level which represents the system nonlinearities considering the approximation error between the fuzzy model and the jump nonlinear system as norm bounded uncertainties we develop a systematic technique based on a coupled lyapunov function to obtain a robust stochastic fuzzy controller which guarantees the l2 gain of the closed loop system in respect to external inputs to be equal to or less than a prescribed value a simulation example on an industrial power plant operating in a cogeneration scheme is presented to illustrate the effectiveness of the proposed stabilizing controller in reducing oscillations as well as maintaining a desired operation condition in the presence of fluctuations in the local load

switched fuzzy output feedback control and its application to a mass spring damping system this paper investigates the dynamic output feedback control problem for interval type 2 it2 fuzzy systems a switched output feedback controller which depends on the values of membership functions is constructed the membership functions of it2 fuzzy systems contain parameter uncertainties and are different from the type 1 takagi sugeno fuzzy systems based on the it2 fuzzy set theory the parameter uncertainties can be effectively obtained by upper and lower membership functions a novel it2 switched output feedback controller is designed to ensure that the closed loop system is asymptotically stable with an h infty performance finally a mass spring damping system is proposed to show the feasibility and the merit of the proposed scheme over the other existing ones

reduced order dynamic output feedback control of continuous time t s fuzzy systems the problem of reduced order dynamic output feedback control design for continuous time takagi sugeno fuzzy systems with h guaranteed cost is addressed the proposed approach is based on a line integral fuzzy lyapunov function with arbitrary polynomial dependence on the premise variables allowing the membership functions modeled as multi simplexes to vary arbitrarily the controller is obtained by transforming the problem into a static output feedback control design problem solved by means of a two stages linear matrix inequality procedure the main appeal of the approach is that the order of the output feedback controller as well as the dependence of the premise variables are customizable for control implementation purposes examples illustrate the flexibility of the method and also that the proposed strategy can provide less conservative results when compared to other methods for full order dynamic output feedback controllers from the literature of continuous time takagi sugeno fuzzy systems

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

hybrid solvers for composition and splitting methods composition and splitting are useful techniques for constructing special purpose integration methods for numerically solving many types of differential equations in this article we will review these methods and summarise the essential ingredients of an implementation that has recently been added to a framework for solving differential equations in mathematica

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

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

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

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

evolving granular fuzzy model based control of nonlinear dynamic systems unknown nonstationary processes require modeling and control design to be done in real time using streams of data collected from the process the purpose is to stabilize the closed loop system under changes of the operating conditions and process parameters this paper introduces a model based evolving granular fuzzy control approach as a step toward the development of a general framework for online modeling and control of unknown nonstationary processes with no human intervention an incremental learning algorithm is introduced to develop and adapt the structure and parameters of the process model and controller based on information extracted from uncertain data streams state feedback control laws and closed loop stability are obtained from the solution of relaxed linear matrix inequalities derived from a fuzzy lyapunov function bounded control inputs are also taken into account in the control system design we explain the role of fuzzy granular data and the use of parallel distributed compensation fuzzy granular computation provides a way to handle data uncertainty and facilitates incorporation of domain knowledge although the evolving granular approach is oriented to control systems whose dynamics is complex and unknown for expositional clarity we consider online modeling and stabilization of the well known lorenz chaos as an illustrative example

robustness design of time delay fuzzy systems using fuzzy lyapunov method abstract in this study we address a fuzzy lyapunov method for the stability analysis of time delay fuzzy systems subject to external disturbances a takagi sugeno t s fuzzy model and parallel distributed compensation pdc scheme are first employed to design a nonlinear fuzzy controller for the stabilization of time delay fuzzy systems according to the controlled system the h criterion is derived based on the fuzzy lyapunov method which is defined in terms of fuzzy blending quadratic lyapunov functions based on the stability criterion the time delay fuzzy systems are guaranteed to be stable the control problem can then be reformulated as a linear matrix inequality lmi problem a simulation is provided to explore the feasibility of the proposed fuzzy controller design method

logic based switching controllers a stepwise safe switching approach the present work proposes a new logic based safe switching technique called here stepwise safe switching this technique is based on the description of the process with linear approximants which are valid in operating areas around a finite number of nominal operating points of the process switching takes place between common controllers for adjacent nominal operating points moreover the switching between the controllers is allowed to take place only when the process has reached an operating point the proposed technique guarantees stability and good performance for all transitions between operating points that lie in the neighborhoods of the nominal operating points of the process this way a simple to design and easy to implement solution that provides good performance despite the drawback of lack of knowledge of the process dynamics can be derived the proposed technique is successfully applied to control an isothermal cstr process described by three linear approximants around corresponding nominal operating points

static output feedback fuzzy controller for chen s chaotic system with uncertainties static output feedback stabilization of chen s chaotic system with uncertainties is studied from a fuzzy control approach an uncertain takagi sugeno ts fuzzy model for the uncertain chen s chaotic system is first constructed then the uncertain ts fuzzy model is represented as a set of uncertain linear systems and a controller design algorithm is proposed specifically a switching static output feedback fuzzy model based controller is designed by solving some linear matrix inequalities lmi which are derived from the developed local representations simulation results have confirmed the effectiveness and feasibility of the proposed modeling and control methods

dynamic output feedback control for continuous time t s fuzzy systems using fuzzy lyapunov functions a novel relaxation approach is proposed for the analysis and dynamic output feedback control of continuous time takagi sugeno t s fuzzy systems using fuzzy lyapunov functions previous relaxation methods for t s fuzzy systems have some drawbacks in relaxing quadratic functions depending on normalized fuzzy weighting functions they often introduce conservatism or lead to computational difficulty in analysis and control synthesis different from previous works the proposed approach employs linear fractional transformation mechanism and full block s procedure to reduce the conservatism in analysis furthermore the relaxation technique proposed in this paper can be used in solving the controller synthesis problem effectively as a result a design procedure of a nonparallel distributed compensation output feedback controller which ensures asymptotic stability and optimizes mathcal l 2 gain performance of the closed loop systems is provided several examples have been used to illustrate the advantages and efficiency of the proposed method extensively

relaxed stability and stabilization conditions of networked fuzzy control systems subject to asynchronous grades of membership this paper presents relaxed stability and stabilization conditions for takagi sugeno t s fuzzy systems under network environments subject to asynchronous grades of membership because of the introduction of a communication network the favorable property in the point to point connection that is sharing the identical premises in the fuzzy plant and the fuzzy controllers cannot be arbitrarily employed to widen the applicability of the fuzzy control method under network environments a novel method is provided to reconstruct the synchronous time scale grades of membership at the controller as those in the plant as a result the aforementioned favorable property can be conditionally used in the derivation of the stability and stabilization criteria for the system under consideration controlled over a communication network numerical examples have been given to illustrate the effectiveness of the proposed approach

functional representations of integrable hierarchies we consider a general framework for integrable hierarchies in lax form and derive certain universal equations from which functional representations of particular hierarchies such as kp discrete kp mkp akns i e formulations in terms of functional equations are systematically and quite easily obtained the formalism genuinely applies to hierarchies where the dependent variables live in a noncommutative typically matrix algebra the obtained functional representations can be understood as noncommutative analogues of fay identities for the kp hierarchy

on additional symmetries of the kp hierarchy and sato s backlund transformation a short proof is given to the fact that the additional symmetries of the kp hierarchy defined by their action on pseudodifferential operators according to fuchssteiner chen lee lin orlov shulman coincide with those defined by their action on functions as sato s backlund transformations a new simple formula for the generator of additional symmetries is also presented

fuzzy robust dynamic output feedback control of nonlinear systems with linear fractional parametric uncertainties in this paper the problem of robust dynamic output feedback control for a class of discrete time nonlinear systems with parametric uncertainties is studied the parametric uncertainties are assumed to be of a linear fractional form first the takagi sugeno t s fuzzy model is employed to represent the nonlinear system then novel approaches are developed to design the dynamic output feedback controller and sufficient conditions for robust stabilization are obtained in the form of linear matrix inequalities lmis the proposed approaches not only have abilities to effectively handle the parametric uncertainties but also are suitable for the fuzzy system with immeasurable premise variables simulation examples are presented to illustrate the design procedures and the effectiveness of the proposed methods