fault detection for uncertain fuzzy systems an lmi approach this paper studies the problem of designing a robust fault detection system for uncertain takagi sugeno fuzzy models the worst case fault sensitivity measure is formulated in terms of linear matrix inequalities the existence of a robust fault detection system that guarantees i the l2 gain from a fault signal to a residual signal greater than a prescribed value and ii the l2 gain from an exogenous input to a residual signal less than a prescribed value is given in terms of the solvability of linear matrix inequalities numerical examples are used to illustrate the effectiveness of the proposed design techniques

design of a polynomial fuzzy observer controller with sampled output measurements for nonlinear systems considering unmeasurable premise variables in this paper we propose a polynomial fuzzy observer controller for nonlinear systems where the design is achieved through the stability analysis of polynomial fuzzy model based pfmb observer control system the polynomial fuzzy observer estimates the system states using estimated premise variables the estimated states are then employed by the polynomial fuzzy controller for the feedback control of nonlinear systems represented by the polynomial fuzzy model the system stability of the pfmb observer control system is analyzed based on the lyapunov stability theory although using estimated premise variables in polynomial fuzzy observer can handle a wider class of nonlinear systems it leads to a significant drawback that the stability conditions obtained are nonconvex matrix decoupling technique is employed to achieve convex stability conditions in the form of sum of squares we further extend the design and analysis to polynomial fuzzy observer controller using a sampled data technique for nonlinear systems where only sampled output measurements are available simulation examples are presented to demonstrate the feasibility and validity of the design and analysis results

stability analysis and control of discrete type 1 and type 2 tsk fuzzy systems part i stability analysis this paper introduces sufficient conditions for the exponential stability of type 1 and type 2 takagi sugeno kang tsk fuzzy systems a major advantage of the new conditions is that they do not require the existence of a common lyapunov function and are therefore applicable to systems with unstable consequents in addition our results include two classes of type 2 tsk systems with type 1 consequents for which no stability tests are available the use of the conditions in stability testing is demonstrated using simple numerical examples that include cases where methods that are based on a common lyapunov function fail the application of the stability test to develop new controller design methodologies is presented in a separate paper i e part ii

lmi based stability analysis for fuzzy model based control systems using artificial t s fuzzy model this paper investigates the stability of fuzzy model based fmb control systems an alternative stability analysis approach using an artificial fuzzy system based on the lyapunov stability theory is proposed to facilitate the stability analysis the continuous membership functions of the takagi sugeno t s fuzzy model are represented by the staircase ones with the nice property of the staircase membership functions it turns the set of infinite number of linear matrix inequality lmi based stability conditions into a finite one furthermore the staircase membership functions carrying system information can be brought to the stability conditions to relax the stability conditions the stability of the original fmb control systems is guaranteed by the satisfaction of the lmi based stability conditions the proposed stability analysis is applied to the fmb control systems of which the t s fuzzy model and fuzzy controller do not share the same premise membership functions and thus is able to enhance the design flexibility of the fuzzy controller a simulation example is given to illustrate the merits of the proposed approach

further studies on h observer design for continuous time takagi sugeno fuzzy model abstract this brief paper is concerned with the problem of observer based h control for nonlinear systems presented by t s takagi sugeno fuzzy models the aim is to reduce the conservatism of finding a smaller h performance index by applying the non quadratic lyapunov function the one step lmis linear matrix inequalities method is applied to design the controller gains and observer gains in addition the initial positions of the observer states are also discussed and an optimization problem is solved to obtain new stable region in the end three examples are given to demonstrate the effectiveness of the proposed approach

output regulation of polynomial fuzzy model based control systems this paper investigates the output regulation problem of polynomial fuzzy model based pfmb control systems with the consideration of system stability and control synthesis using the sum of squares sos based approach a pfmb control system is formed by a polynomial fuzzy model and a polynomial fuzzy controller with integral action connected in a closed loop three cases of pfmb control systems regarding the premise membership functions and number of fuzzy rules which have their own properties and advantages are considered the stability of the pfmb control systems is investigated based on the lyapunov stability theory with consideration of the information of membership functions sos based stability conditions corresponding to each case are obtained to guarantee system stability and to realize output regulation simulation examples are given to compare the three cases and illustrate the effectiveness of the proposed approach

robust static output feedback h control for uncertain fuzzy systems this paper will focus on robust static output feedback sof h control for discrete time takagi sugeno t s fuzzy systems with time varying norm bounded uncertainties first a new h performance analysis criterion is proposed for the fuzzy systems then sufficient conditions for designing fuzzy sof h controllers are given in terms of solutions to a set of linear matrix inequalities lmis in contrast to the existing methods for designing the sof h controllers the output matrices of the considered fuzzy system are allowed to be non common and to have uncertainties moreover theoretical proof is given to show that the proposed design conditions include some existing results as special cases simulation examples are provided to show the effectiveness of the proposed design method

observer design of discrete time t s fuzzy systems via multi instant homogenous matrix polynomials this paper is concerned with the design of observer for discrete time nonlinear systems in the takagi sugeno t s fuzzy form under the framework of multi instant homogenous matrix polynomials a novel fuzzy observer and a new lyapunov function which are homogenous polynomially parameter dependent on both the current time normalized fuzzy weighting functions and the m steps past time normalized fuzzy weighting functions are proposed for conceiving less conservative observer design conditions since the algebraic properties of both the current time normalized fuzzy weighting functions and the m steps past time normal ized fuzzy weighting functions are fully considered the relaxation quality of the fuzzy observer design of discrete time t s fuzzy systems is significantly improved in particular some existing fuzzy lyapunov functions and fuzzy observers are special cases of the lyapunov function and the fuzzy observer given in this paper respectively finally a numerical example is provided to illustrate the effectiveness of the proposed approach index terms discrete time system homogenous matrix polynomials multi instant observer design takagi sugeno t s fuzzy model

stabilization of takagi sugeno models with non measured premises input to state stability approach abstract this work deals with the observer based output stabilization problem for takagi sugeno models with non measured premises it aims at providing efficient design methods for the controller observer pair with minimal constrained hypothesis on the model non linear functions the main idea is to consider the closed loop and the error dynamic as two interacting subsystems and study them in the input to state stability framework this paper provides also some results about the existence of a stabilizing output feedback for all models of a sub class of takagi sugeno models to illustrate the efficiency of the proposed design procedures illustrative examples and a comparative study with existing results in the literature based on more restrictive hypothesis are presented

nonfragile h_ infty filtering of continuous time fuzzy systems this paper is concerned with the problem of nonfragile h filtering for a class of continuous time fuzzy systems attention is focused on the design of a filter such that the filtering error system preserves a prescribed h performance where the filter to be designed is assumed to have gain variations by using the quadratic lyapunov function approach and adding slack matrix variables sufficient conditions for designing the nonfragile h filter are proposed in terms of solutions to a set of linear matrix inequalities lmis finally a simulation example will be given to show the efficiency of the proposed design methods

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

control synthesis of discrete time t s fuzzy systems based on a novel non pdc control scheme this paper proposes relaxed stabilization conditions of discrete time nonlinear systems in the takagi sugeno t s fuzzy form by using the algebraic property of fuzzy membership functions a novel nonparallel distributed compensation non pdc control scheme is proposed based on a new class of fuzzy lyapunov functions thus relaxed stabilization conditions for the underlying closed loop fuzzy system are developed by applying a new slack variable technique in particular some existing fuzzy lyapunov functions and non pdc control schemes are special cases of the new lyapunov function and fuzzy control scheme respectively finally two numerical examples are provided to illustrate the effectiveness of the proposed method

an efficient approach for reducing the conservatism of lmi based stability conditions for continuous time t s fuzzy systems this paper deals with reducing the conservatism of stability conditions for continuous time t s fuzzy systems previous stability conditions are relaxed by further exploring the properties of the time derivatives of normalized fuzzy weighting functions and by introducing more slack matrix variables by relying on analysis of the positive and negative characteristics of the time derivatives of normalized fuzzy weighting functions some redundant terms are removed from the problem formulation furthermore more slack matrix variables are introduced to enlarge the design space consequently less conservative stability conditions are obtained finally a well known numerical example is provided to illustrate the effectiveness of the proposed result

further improvement of periodic control approach for relaxed stabilization condition of discrete time takagi sugeno fuzzy systems in this paper we present a new stabilization condition for discrete time takagi sugeno t s fuzzy systems to this end the previously developed periodic nonparallel distributed compensation non pdc control law is extended to the more general one whose gain matrix has a block lower triangular matrix form a distinguished feature of the proposed control law is that it uses a discrete time feedback loop incorporating information from the previous states of the system the resultant stabilization condition is represented in the form of linear matrix inequalities lmis in addition we show that the proposed condition includes the existing one based on the periodic control approach as a particular case finally examples are given to show that the proposed condition provides less conservative results than those of the existing ones published in the literature

interval type 2 fuzzy model predictive control of nonlinear networked control systems in this paper the problem of fuzzy predictive control of nonlinear networked control systems subject to parameter uncertainties and defective communication links is studied stochastic variables with bernoulli random binary distribution are used to represent the defective communication links with packets loss occurring intermittently between the controller and the physical plant an interval type 2 it2 takagi sugeno t s fuzzy model is employed to describe the nonlinear plant subject to parameter uncertainties which can be captured with the lower and upper membership functions the it2 fuzzy model and it2 fuzzy controller are not required to share the same lower and upper membership functions in order to design the state feedback fuzzy model predictive controller an optimization problem which minimizes the upper bound of a quadratic objective function subject to input constraints and packets dropout is formulated and solved at every sampling instant in the finite time horizon by introducing some slack matrices less conservative conditions are developed for system stability analysis two examples are given to demonstrate the effectiveness and merits of the proposed new design techniques

local stability analysis of continuous time takagi sugeno fuzzy systems a fuzzy lyapunov function approach this paper proposes a strategy to estimate invariant subsets of the domain of attraction da for asymptotically stable zero equilibrium points of continuous time takagi sugeno t s fuzzy systems specifically by using lyapunov s stability theory and the linear matrix inequality lmi technique sufficient conditions for proving the local stability are provided in terms of single parameter minimization problems subject to lmi constraints or eigenvalue problems which are solvable via convex optimizations the fuzzy lyapunov functions flfs expressed by the so called multi dimensional fuzzy summations are employed to characterize invariant subsets of the da as sublevel sets of the flfs to compute a larger inner estimate of the da an iterative lmi algorithm is also developed finally illustrative examples show the efficacy of the approach

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

a fuzzy lyapunov function approach to estimating the domain of attraction for continuous time takagi sugeno fuzzy systems this paper deals with stability analysis and control design problems for continuous time takagi sugeno t s fuzzy systems the first aim is to present less conservative linear matrix inequality lmi conditions to design controllers and assess the stability the second relevant contribution is to present a new strategy to find an inner estimate of the domain of attraction da via lmis the results are based on the fuzzy lyapunov functions flfs and non parallel distributed compensation non pdc approaches finally examples illustrate the effectiveness and merits of the proposed methods

stability analysis of polynomial fuzzy model based control systems with mismatched premise membership functions this paper investigates the stability of polynomial fuzzy model based pfmb control system which is formed by a polynomial fuzzy model and a polynomial fuzzy controller connected in a closed loop to enhance the design flexibility the number of rules and the shape of premise membership functions of the polynomial fuzzy controller are considered to be chosen freely and are different from those of the polynomial fuzzy model however which make the stability analysis more difficult and potentially lead to conservative stability analysis result a sum of squares sos based stability analysis approach using the lyapunov stability theory is proposed to investigate the stability of the pfmb control systems and synthesize the polynomial fuzzy controller to facilitate the stability analysis and relax the stability analysis result the property of the membership functions and the boundary information of the membership grades and premise variables are taken into account in the stability analysis and incorporated into the sos based stability conditions a simulation example is given to illustrate the effectiveness of the proposed approach

t s model based nonlinear moving horizon h control and applications using a t s fuzzy model we propose a formulation for a moving horizon h control problem for nonlinear systems our main contribution is combination of t s fuzzy models and a moving horizon h control scheme by chen and scherer to address the disturbance attenuation of nonlinear constrained system a sufficient condition for the disturbance amplitude is given to guarantee the feasibility of the optimization problem at each time a parameter dependent state feedback control law is adopted and the corresponding optimization problem is reduced to a convex optimization problem involving linear matrix inequalities lmis the h attenuation index for the nonlinear moving horizon h control problem is adapted online to satisfy time domain constraints finally the effectiveness of the proposed scheme is successfully demonstrated by control of a continuous stirred tank reactor and active queue management for routers

robust stabilizing controller design for takagi sugeno fuzzy descriptor systems under state constraints and actuator saturation abstract the aim of this paper is to present a new framework for designing robust controllers for uncertain nonlinear systems described by takagi sugeno fuzzy descriptor systems and subject to input and state constraints for this a novel structure of modified parallel distributed compensation control laws is proposed the controller parameters can be obtained through the numerical resolution of an optimization problem with linear matrix inequality constraints derived from lyapunov s stability theory and the choice of an original lyapunov function this ensures the stabilization of the closed loop system and the respect of the state and input constraints regionally the technique is illustrated through three numerical examples

relaxed stability and performance lmi conditions for takagi sugeno fuzzy systems with polynomial constraints on membership function shapes most linear matrix inequality lmi fuzzy control results in literature are valid for any membership function i e independent of the actual membership shape hence they are conservative with respect to other nonlinear control approaches when specific knowledge of the shapes is available this paper presents relaxed lmi conditions for fuzzy control that incorporate such shape information in the form of polynomial constraints generalizing previous works by the authors interesting particular cases are overlap product bounds and ellipsoidal regions numerical examples illustrate the achieved improvements as well as the possibilities of solving some multiobjective problems the results also apply to polynomial in membership takagi sugeno fuzzy systems

fuzzy static output feedback may be possible in lmi framework takagi sugeno t s fuzzy model based static output feedback controller design is a challenging issue due to the nonconvexity in the lyapunov stability condition recently a convexified linear matrix inequality lmi condition was proposed for the problem by additionally importing as many equality constraints as the number of the fuzzy rules with a variable in the paper from the study of fang et al however numerical experiences seem to imply the infeasibility of the proposed lmi this letter shows that their lmi problem may be feasible

a descriptor representation approach to observer based h control synthesis for discrete time fuzzy systems this work is concerned with the observer based h control synthesis problem of discrete time takagi sugeno t s fuzzy systems with external disturbances the objective is to find a new way to design the controller and observer guaranteeing a prescribed h performance of the fuzzy system by the descriptor representation approach two new conditions for observer based h control synthesis are proposed based on various lyapunov function candidates which are in the form of linear matrix inequalities lmis a numerical example will be given to show the efficiency of the proposed method

brief paper approaches to extended non quadratic stability and stabilization conditions for discrete time takagi sugeno fuzzy systems this paper provides simple and effective linear matrix inequality lmi characterizations for the stability and stabilization conditions of discrete time takagi sugeno t s fuzzy systems to do this more general classes of non parallel distributed compensation non pdc control laws and non quadratic lyapunov functions are presented unlike the conventional non quadratic approaches using only current time normalized fuzzy weighting functions we consider not only the current time fuzzy weighting functions but also the l step past l 0 and one step ahead ones when constructing the control laws and lyapunov functions consequently by introducing additional decision variables it can be shown that the proposed conditions include the existing ones found in the literature as particular cases examples are given to demonstrate the effectiveness of the approaches

a triangulation approach to asymptotically exact conditions for fuzzy summations many takagi sugeno t s fuzzy control synthesis problems in the literature are expressed as the problem of finding decision variables in a double convex sum fuzzy summation of positive definite matrices matricespsila coefficients in the summation take values in the standard simplex this paper presents a triangulation approach to the problem of generating simplicial partitions of the standard simplex in order to set up a family of sufficient conditions and in parallel another family of necessary ones for fuzzy summations the conditions proposed in this paper are asymptotically exact as the size of the involved simplices decreases its conservativeness vanishes for a sufficiently fine partition sufficiently dense mesh of vertex points the set of conditions is in the form of linear matrix inequalities lmis for which efficient software is available

improvement on nonquadratic stabilization of discrete time takagi sugeno fuzzy systems multiple parameterization approach this paper presents the relaxed nonquadratic stabilization conditions of discrete time takagi sugeno t s fuzzy systems to do this we propose a new fuzzy controller and lyapunov function by generalizing the nonparallel distributed compensation non pdc control law and nonquadratic lyapunov function respectively by exploiting po lya s theorem and algebraic properties of a homogeneous polynomials of normalized fuzzy weighting functions an infinite family of sufficient conditions for the asymptotic stabilizability is derived these conditions are formulated in the format of linear matrix inequalities lmis and hence are numerically tractable via convex programming techniques finally an example is given to illustrate advantages of the proposed method

cal h _ infty state feedback control design for fuzzy systems using lyapunov functions with quadratic dependence on fuzzy weighting functions this paper proposes a method for designing an hinfin state feedback fuzzy controller for discrete time takagi sugeno t s fuzzy systems to derive less conservative hinfin stabilization conditions this paper enhances the interactions among the fuzzy subsystems using a multiple lyapunov function with quadratic dependence on fuzzy weighting functions besides for more allocation of the nonlinearity to the fuzzy control system this paper introduces a slack variable that is quadratically dependent on the one step past fuzzy weighting functions as well as the current ones in the derivation the hinfin stabilization conditions are formulated in terms of parameterized linear matrix inequalities plmis which are reconverted into lmi conditions with the help of an efficient relaxation technique

a new lmi based approach to relaxed quadratic stabilization of t s fuzzy control systems this paper proposes a new quadratic stabilization condition for takagi sugeno t s fuzzy control systems the condition is represented in the form of linear matrix inequalities lmis and is shown to be less conservative than some relaxed quadratic stabilization conditions published recently in the literature a rigorous theoretic proof is given to show that the proposed condition can include previous results as special cases in comparison with conventional conditions the proposed condition is not only suitable for designing fuzzy state feedback controllers but also convenient for fuzzy static output feedback controller design the latter design work is quite hard for t s fuzzy control systems based on the lmi based conditions derived one can easily synthesize controllers for stabilizing t s fuzzy control systems since only a set of lmis is involved the controller design is quite simple and numerically tractable finally the validity and applicability of the proposed approach are successfully demonstrated in the control of a continuous time nonlinear system

qualitative behaviour and stability of solutions of discretised nonlinear volterra integral equations of convolution type abstract in this work we consider equations of the form y t g t t o k t s y s ds te r and their discretised versions obtained through application of quadrature to of the form y n g n h j 0 n w n j j j y j n j e n subject to certain conditions on k g and the weights wj one purpose of the paper is to show how the discussion of qualitative behaviour and stability for can be mimicked in a discussion of we first describe corduneanu s 1973 discussion of stability for re presenting his material in a modified form which lends itself to adaptation for our discussion of we give a stability result for we then demonstrate the stability behaviour of some simple quadrature rules applied to an illustrative example equation and we observe that for a particular family of quadrature rules the qualitative behaviour of solutions to the example equation is preserved under the discretisation

new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi the problems of relaxed quadratic stability conditions fuzzy observer designs and h controller designs for t s fuzzy systems have been studied first new stability conditions are obtained by relaxing the stability conditions derived in previous papers secondly new fuzzy observers based on the relaxed stability conditions for the t s fuzzy systems have been proposed thirdly two sufficient lmi conditions which guarantee the existence of the h controllers based on fuzzy observers for the t s fuzzy systems have been proposed the conditions are not only simple but also consider the interactions among the fuzzy subsystems finally by some examples using the lmi technique we show that the regulators the fuzzy observers and the h controller designs based on new observers for the t s fuzzy systems are very practical and efficient

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

an efficient lyapunov function for discrete t s models observer design this paper deals with the design of a new observer synthesis for discrete takagi sugeno t s fuzzy models it is well established that quadratic synthesis for discrete t s models and or linear parameter varying systems can be outperformed easily via nonquadratic syntheses several lyapunov functions can be used nevertheless this paper shows that with a small change in the initial lyapunov function a better in the sense of solutions to the linear matrix inequality constraints problem lyapunov function can be reached this one can introduce very important improvements

a new fuzzy lyapunov function for relaxed stability condition of continuous time takagi sugeno fuzzy systems this paper presents a new fuzzy lyapunov function flf for the stability analysis of continuous time takagi sugeno t s fuzzy systems unlike conventional flfs the proposed one depends not only on the fuzzy weighting functions of the t s fuzzy systems but on their first order time derivatives as well based on the proposed flf a sufficient stability condition is derived in the form of linear matrix inequalities depending on the upper bounds on the second order time derivative of the fuzzy weighting functions as well as the first order ones finally some examples demonstrate that the proposed condition can provide less conservative results than the previous ones in the literature

a scaling theory of clusters in the lattice gas it is proposed that the number ofp particle k bond lattice gas cluster configurations is of the form exp pf k p in the limitp t8 a simple modification permits application to finite clusters with the consequence that asymptotically the cluster partition function is of the droplet form i e z p exp kp it p1 1 d o ln p the scaling function for two dimensional lattices is determined numerically and is found to be qualitatively universal the scaling theory is used to investigate the size dependence of the surface free energy the surface tension of small clusters can significantly exceed its limiting value for intermediate cluster sizes 100 particles there is a modest reduction in surface tension in accord with tolman s prediction and the results of recent monte carlo studies

fuzzy filter design for nonlinear systems in finite frequency domain this paper is concerned with the problem of fuzzy filter design for discrete time nonlinear systems in the takagi sugeno t s form different from existing fuzzy filters the proposed ones are designed in finite frequency domain first a so called finite frequency l2 gain is defined that extends the standard l2 gain then a sufficient condition for the filtering error system with a finite frequency l2 gain is derived based on the obtained condition three fuzzy filters are designed to deal with noises in the low middle and high frequency domain respectively the proposed fuzzy filtering method can get a better noise attenuation performance when frequency ranges of noises are known beforehand an example about a tunnel diode circuit is given to illustrate its effectiveness

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

relaxed stabilization criterion for t s fuzzy systems by minimum type piecewise lyapunov function based switching fuzzy controller this paper proposes the minimum type piecewise lyapunov function based switching fuzzy controller that switches accompanying the piecewise lyapunov function by applying this switching fuzzy controller with the minimum type piecewise lyapunov function the relaxed stabilization criterion is obtained for continuous takagi sugeno t s fuzzy systems some conditions of the relaxed stabilization criterion are represented by bilinear matrix inequalities bmis which contain some bilinear terms as the product of a full matrix and a scalar according to the literature the path following method is very effective for this kind of bmi problem hence it is utilized to obtain solutions of the criterion xie et al in 1997 chose two types i e minimum type and maximum type of piecewise lyapunov functions as the lyapunov function candidates the reasons for why this study only chooses the minimum type piecewise lyapunov function as the lyapunov function candidate are illustrated moreover the numerical example shows the relaxation of the proposed criterion

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

convergent lmi relaxations for quadratic stabilizability and mathscr h _ infty control of takagi sugeno fuzzy systems this paper investigates the quadratic stabilizability of takagi sugeno t s fuzzy systems by means of parallel distributed state feedback compensators using finsler s lemma a new design condition assuring the existence of such a controller is formulated as a parameter dependent linear matrix inequality lmi with extra matrix variables and parameters in the unit simplex algebraic properties of the system parameters and recent results of positive polynomials are used to construct lmi relaxations that differently from most relaxations in the literature provide certificates of convergence to solve the control design problem due to the degrees of freedom obtained with the extra variables the conditions presented in this paper are an improvement over earlier results based only on polya s theorem and can be viewed as an alternative to the use of techniques based on the relaxation of quadratic forms an extension to cope with guaranteed h infin attenuation levels is also given with proof of asymptotic convergence to the global optimal controller under quadratic stability the efficiency of the proposed approach in terms of precision and computational effort is demonstrated by means of numerical comparisons with other methods from the literature

on local h switched controller design for uncertain t s fuzzy systems subject to actuator saturation with unknown membership functions abstract this manuscript proposes a local h switched controller design for a class of uncertain nonlinear plants described by takagi sugeno t s fuzzy models with unknown membership functions the control design requires only the lower and upper bounds of the system nonlinearities and of the system linear parameters which can depend on uncertain parameters the switched control law chooses a state feedback controller gain which belongs to a given set of gains that minimizes the time derivative of a quadratic lyapunov function this procedure eliminates the necessity of finding the membership function expressions to implement the control law guarantees an h performance and ensures that the state trajectory remains within a region in which the t s fuzzy model is valid due to the h control design that frequently results in very large control inputs it is considered that the switched control law is subject to actuator saturation finally two examples are presented the first example studies the control of a chaotic lorenz system it shows that for disturbances with large magnitude the proposed procedures provided better results than the obtained with another recent method found in the literature that considers full access to the membership functions in the second example a practical implementation of an active nonlinear suspension control system considering an uncertain bounded mass and a fault in the actuator confirms the effectiveness of the proposed approach

relaxed lmi based stability conditions for takagi sugeno fuzzy control systems using regional membership function shape dependent analysis approach this paper presents relaxed stability conditions for takagi sugeno t s fuzzy model based control systems it is assumed that the stability conditions are represented by some inequalities in the form of a p dimensional fuzzy summation to investigate the system stability the inequalities are expanded to n dimensional fuzzy summation n ges p the boundary and regional informations of membership functions are then utilized for relaxation of stability analysis results two analysis approaches are proposed in this paper the first approach is called the global membership function shape dependent approach in which the lower and upper bounds of the membership functions and its products from 2 to n in the full operating domain are considered in the stability analysis the second approach is named as the regional membership function shape dependent approach in which the operating region is partitioned to subregions and the boundary information of membership functions on each operating subregion is employed to facilitate the stability analysis in both approaches by the help of the boundary and or regional information of the membership functions some inequality constraints in the form of multidimensional fuzzy summation containing some slack matrices are constructed stability conditions in the form of linear matrix inequalities lmis are derived numerical examples are given to demonstrate the effectiveness of the proposed stability conditions

on the generalized local stability and local stabilization conditions for discrete time takagi sugeno fuzzy systems in this paper local stability and local stabilization problems are considered for discrete time nonlinear systems represented by takagi sugeno t s fuzzy systems improved methods to assess the local stability design locally stabilizing control laws and estimate the domain of attraction are developed in terms of single parameter minimization problems subject to linear matrix inequality lmi constraints the improvement is achieved by applying a convergent lmi relaxation technique to prove positivity of homogeneous polynomial parameter dependent matrices of arbitrary degree with variables in the simplex we also take advantage of the recently developed parameter variation modeling technique to deal with the case that the variation rate of the membership functions of the t s fuzzy systems is bounded and less than one finally several illustrative examples demonstrate the validity and efficiency of the proposed method

relaxation technique for a t s fuzzy control design based on a continuous time fuzzy weighting dependent lyapunov function based on the fuzzy weighting dependent lyapunov function this paper proposes a method to drive the relaxed stabilization condition for continuous time takagi sugeno t s fuzzy control systems without resorting to elimination and bounding techniques here to achieve an improved robust h performance while enhancing the interactions among the fuzzy subsystems this paper proposes a valuable relaxation technique that is capable of incorporating the derivatives of fuzzy weighting functions to the relaxation process finally three examples are given to verify the effectiveness of the proposed method

new approach on robust delay dependent h _ infty control for uncertain t s fuzzy systems with interval time varying delay this paper investigates the robust h infin control for takagi sugeno t s fuzzy systems with interval time varying delay by employing a new and tighter integral inequality and constructing an appropriate type of lyapunov functional delay dependent stability criteria are derived for the control problem because neither any model transformation nor free weighting matrices are employed in our theoretical derivation the developed stability criteria significantly improve and simplify the existing stability conditions also the maximum allowable upper delay bound and controller feedback gains can be obtained simultaneously from the developed approach by solving a constrained convex optimization problem numerical examples are given to demonstrate the effectiveness of the proposed methods

relaxed stability and stabilization conditions for a t s fuzzy discrete system it is known that the stability condition of a t s fuzzy discrete system depends on the existence of the common matrix p which satisfies all lyapunov inequalities in general the common matrix p can be found by means of linear matrix inequalities lmi method however if the number of rules of a fuzzy system is large the common matrix p may not exist or may not be found even using lmi therefore in this paper the state space is divided into several subregions and the local common matrix p j for each subregion j is found then the number of lyapunov inequalities to be satisfied by the corresponding local common matrix p j becomes much fewer such that the stability condition of the fuzzy system is more relaxed the similar derivation is also extended to solve the stabilization problem of the t s fuzzy discrete system with parallel distributed compensation

observer based relaxed cal h _ infty control for fuzzy systems using a multiple lyapunov function this short paper proposes a method of designing a fuzzy observer based h infin controller for discrete time takagi sugeno t s fuzzy systems to enhance the applicability of the output feedback controller and improve its performance this short paper first builds a set of fuzzy control rules with premise variables different from those of the t s fuzzy system and sets the overall controller to be dependent on not only the current time but also the one step past information on the estimated fuzzy weighting functions then based on the fuzzy control rules this short paper establishes a less conservative h infin stabilization condition incorporated with a multiple lyapunov function dependent on the estimated fuzzy weighting functions through a two step design procedure the h infin stabilization condition is formulated in terms of parameterized linear matrix equalities plmis which are reconverted into lmis with the help of an efficient and effective relaxation scheme

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

a robust h_ infty non pdc design scheme for singularly perturbed t s fuzzy systems with immeasurable state variables this paper addresses an observer based robust h infty fuzzy controller design method for singularly perturbed nonlinear systems with external disturbances which are represented by uncertain takagi sugeno t s fuzzy models for a practical output feedback design the premise variables of the fuzzy controller and the fuzzy observer are considered unknown in general a fuzzy lyapunov function is utilized for the synthesis of the nonparallel distributed compensation based controller the closed loop singularly perturbed t s fuzzy system is asymptotically robustly stable in the absence of disturbances and satisfies an h infty norm condition in the presence of disturbances for all positive values of the singular perturbation parameter within the given desired bound using the descriptor redundancy approach some strict linear matrix inequality lmi conditions are derived for the h infty robustness of the closed loop system when uncertainties are simultaneously considered in all state space matrices of each fuzzy subsystem the main disadvantage of a fuzzy lyapunov function based design is that the bounds on the derivatives of the membership functions must be known a priori inspired by a recent work that provides the bounds of the membership derivatives for a given arbitrary compact set on the state space a new method is proposed that guarantees that the closed loop observer based uncertain singularly perturbed t s fuzzy system remains robustly stable in the compact set using finsler s lemma the resulting design conditions are converted to lmis two numerical examples are provided to show the effectiveness of the proposed method

membership function dependent stability analysis of fuzzy model based control systems using fuzzy lyapunov functions this paper investigates the stability of fuzzy model based fmb control system formed by a t s fuzzy model and a fuzzy controller connected in a close loop based on a fuzzy lyapunov function a general fmb control system that the t s fuzzy model and fuzzy controller not sharing the same premise membership functions and or the same number of fuzzy rules is considered a membership function dependent stability analysis approach is proposed to consider the membership functions of both the t s fuzzy model and fuzzy controller in the stability analysis and incorporate them in the stability conditions in the form of linear matrix inequalities as the stability conditions are membership function dependent they are dedicated to the fmb control system with the specified membership functions under consideration it is thus the membership function dependent stability conditions are more relaxed compared to the existing membership function independent stability conditions a fuzzy lyapunov function is a weighted sum of quadratic functions which are required to be positive definite in most of the existing work in this paper this criterion is not required and thus the stability conditions can be further relaxed some simulation examples are given to demonstrate the merits of the proposed approach

asymptotically necessary and sufficient conditions for stability and performance in fuzzy control applications of polya s theorem stability and performance requirements in fuzzy control of takagi sugeno systems are usually stated as fuzzy summations i e sums of terms related to lyapunov functions which are weighted by membership functions or products of them this paper presents an application to fuzzy control of polya s theorems on positive forms on the standard simplex the result provides a set of progressively less conservative sufficient conditions for proving positivity of fuzzy summations such conditions are less and less conservative as a complexity parameter n increases particular cases of such conditions are those in c h fang y s liu s w kau l hong c h lee a new lmi based approach to relaxed quadratic stabilization of t s fuzzy control systems ieee trans fuzzy systems 14 2006 286 397 x liu q zhang new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi automatica 39 9 2003 1571 1582 with n 2 and 3 respectively the proposed conditions are asymptotically exact i e necessary and sufficient when n tends to infinity or equivalently when a tolerance parameter tends to zero

on switched regulator design of uncertain nonlinear systems using takagi sugeno fuzzy models this paper is concerned with the design of state feedback switched controllers for a class of uncertain nonlinear plants described by takagi sugeno t s fuzzy models the proposed methodology eliminates the need to find the membership function expressions to implement the control law which is relevant in cases where the membership function depends on uncertain parameters the design of the switched controllers is based on a minimum type lyapunov function and the minimization of the time derivative of this lyapunov function the conditions of the new stability criterion are represented by a kind of bilinear matrix inequalities bmis that has been solved by the path following method a numerical example and the nonlinear control design of a magnetic levitator with uncertainties illustrate the procedure

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

robust nonfragile h_ infty filtering of fuzzy systems with linear fractional parametric uncertainties this paper is concerned with the h filtering problem for continuous time takagi sugeno t s fuzzy systems different from existing results for fuzzy h filtering the proposed ones are toward uncertain fuzzy systems with linear fractional parametric uncertainties attention is focused on the design of a fuzzy filter such that the filtering error system preserves a prescribed h performance where the filter to be designed is assumed to have gain variations by a descriptor representation approach two sufficient conditions for the h filter design are proposed in terms of linear matrix inequalities lmis when these lmis are feasible an explicit expression of the desired filter is given a simulation example will be given to show the efficiency of the proposed 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

selective hbox scr h _2 and hbox scr h _ infty stabilization of takagi sugeno fuzzy systems this paper presents new results concerning the stability analysis and design of state feedback controllers for continuous time takagi sugeno t s fuzzy systems via fuzzy lyapunov functions the membership functions of the t s fuzzy systems are modeled in a space that is defined by the cartesian product of simplexes called a multisimplex if the time derivatives of the membership functions are bounded the bounds are used to construct a polytope that models the space of the time derivatives of the membership functions linear matrix inequality lmi relaxations that are based on polynomial matrices are provided for stability analysis and controller design extensions for the design of control laws that minimize upper bounds to h2 and h norms are also given the main novelty of this method is that it allows one to synthesize control gains which depends only on some premise variables that are selected by the designer numerical experiments illustrate the flexibility and advantages of the proposed method

delay dependent h fuzzy observer based control for discrete time nonlinear systems with state delay this paper studies the h fuzzy observer based control problem for discrete time nonlinear systems with state delay via a fuzzy lyapunov krasovskii functional lkf approach the takagi and sugeno t s fuzzy model is employed to represent a discrete time nonlinear system with state delay based on a non parallel distributed compensation pdc scheme a new fuzzy lkf is first constructed to derive a delay dependent condition such that the closed loop fuzzy system is asymptotically stable and satisfies a prescribed level of h disturbance attenuation in the derivation process two free fuzzy weighting matrices are introduced to express the relationship between the present state and delay state then a novel linear matrix inequality lmi approach is proposed for the design of a delay dependent h fuzzy observer based controller the control and observer matrices can be solved directly by using the existing lmi optimization techniques finally a numerical example is given to illustrate the effectiveness of the proposed design method

an approach to observer design of continuous time takagi sugeno fuzzy model with bounded disturbances this paper addresses the problem of designing the observer for a class of nonlinear systems by using the t s takagi sugeno fuzzy model first two lemmas are obtained to demonstrate how to design the observer then based on the non quadratic lyapunov function a new method is proposed to locally stabilize the t s fuzzy system the new method can be applied to any t s models no matter whether the rules are even or odd naturally the new method is extended to get some lmis linear matrix inequalities to design the observer for practical reason the disturbances considered in this paper are bounded by magnitude and energy finally three examples are given to illustrate the effectiveness of the new approach

polynomial fuzzy model based control systems stability analysis via approximated membership functions considering sector nonlinearity of control input this paper presents the stability analysis of polynomial fuzzy model based pfmb control systems in which both the polynomial fuzzy model and the polynomial fuzzy controller are allowed to have their own set of premise membership functions in order to address the input nonlinearity the control signal is considered to be bounded by a sector with nonlinear bounds these nonlinear lower and upper bounds of the sector are constructed by combining local bounds using fuzzy blending such that local information of input nonlinearity can be taken into account with the consideration of imperfectly matched membership functions and input nonlinearity the applicability of the pfmb control scheme can be further enhanced to facilitate the stability analysis a general form of approximated membership functions representing the original ones is introduced as a result approximated membership functions can be brought into the stability analysis leading to relaxed stability conditions the sum of squares approach is employed to obtain the stability conditions based on lyapunov stability theory simulation examples are presented to demonstrate the feasibility of the proposed method

local analysis of continuous time takagi sugeno fuzzy system with disturbances bounded by magnitude or energy a lagrange multiplier method abstract this paper is concerned with the problem of computing the bounds of disturbances for continuous time takagi sugeno fuzzy model two kinds of disturbances are investigated by applying the non parallel distributed compensation non pdc law non quadratic lyapunov function and lagrange multiplier method one is bounded by magnitude the other is bounded by energy if the exogenous disturbances are bounded by magnitude the maximal value of the magnitude under which the closed loop system can be controlled is obtained by solving an optimization problem on the other hand if the disturbances are bounded by energy except for the maximal bound some conditions are derived to get two local regions a smaller and a bigger such that all the trajectories starting from the smaller region will remain in the bigger one which is required to be contained in a specific compact set where the original system can be represented as t s model exactly in the end the effectiveness of the proposed results is demonstrated by two examples

homogeneous polynomially nonquadratic stabilization of discrete time takagi sugeno systems via nonparallel distributed compensation law this paper considers stability of discrete time nonlinear systems in takagi sugeno t s form this problem has been studied for more than 20 years with many sufficient conditions and the asymptotically necessary and sufficient ans conditions with respect to the common quadratic lyapunov function having being obtained this paper considers general forms of homogeneous polynomially nonquadratic lyapunov hpnql function and homogeneous polynomially parameterized nonparallel distributed compensation hpp non pdc law by generalization of the procedure based on polya s theorem and techniques used for parameter dependent linear matrix inequality pd lmi which have been studied previously in different contexts ans stability conditions with respect to the general hpnql function are obtained

stability analysis of t s fuzzy control systems by using set theory this paper is concerned with the stability analysis for takagi sugeno t s fuzzy control systems by exploiting the property of the structure of a fuzzy inference engine an equivalence relation on the index set of the product of fuzzy rule weights is defined furthermore a new stability criterion is proposed by using the equivalence relation and formulated into progressively less conservative sets of linear matrix inequalities by using an extension of polya s theorem the new criterion is proved to be with no conservatism for quadratic stability analysis of t s fuzzy control systems with a product inference engine and any possible fuzzy membership functions a numerical example is given to illustrate the effectiveness of the proposed method

on relaxed lmi based designs for fuzzy regulators and fuzzy observers relaxed conditions for stability of nonlinear continuous and discrete time systems given by fuzzy models are presented a theoretical analysis shows that the proposed methods provide better or at least the same results of the methods presented in the literature numerical results exemplify this fact these results are also used for fuzzy regulators and observers designs the nonlinear systems are represented by fuzzy models proposed by takagi and sugeno 1985 the stability analysis and the design of controllers are described by linear matrix inequalities that can be solved efficiently using convex programming techniques the specification of the decay rate constrains on control input and output are also discussed

relaxed stability conditions for continuous time t s fuzzy control systems via augmented multi indexed matrix approach this paper is concerned with the problem of developing an advanced strategy to reduce the conservatism in stability analysis and control synthesis of continuous time takagi sugeno t s fuzzy systems a novel augmented multi indexed matrix approach is proposed to implement new right hand side slack variables technique for the homogenous polynomial setting combining with the finsler lemma with homogenous matrix lagrange multipliers convergent linear matrix inequality lmi relaxations for stability analysis are proposed by using the generalization of the polya theorem for the case of positive polynomials with matrix valued coefficients a new type of state feedback controller namely the homogeneous polynomially nonquadratic control law hpnqcl is developed to conceive less conservative stabilization conditions the obtained stability and stabilization conditions are further relaxed by using the proposed right hand side slack variables technique moreover the advantages over the existing control schemes are certificated in theory three numerical examples are also provided to illustrate the effectiveness of the proposed methods

sos based stability analysis of polynomial fuzzy model based control systems via polynomial membership functions this paper presents stability analysis of polynomial fuzzy model based fmb control systems using the sum of squares sos approach recently stability analysis of the polynomial fuzzy control systems which is a generalized form of the well known takagi sugeno t s fmb control systems has been reported in the form of sos based stability conditions lack of information on the relations between membership functions and premise variables in the existing stability analysis approaches causes conservatism of their results in this paper to derive relaxed stability conditions for polynomial fmb control systems membership functions which are approximated with polynomials and carrying relations between membership functions and premise variables are brought into the stability analysis considering a polynomial fmb control system and based on the lyapunov stability theory stability conditions in the form of fuzzy summations are derived where each term contains product of membership functions of the polynomial fuzzy model and polynomial fuzzy controller each product term is approximated by a polynomial in order to obtain better approximation the operating domain of membership functions is partitioned to subregions then sos based stability conditions for all subregions are derived unlike some published stability analysis approaches the proposed one can be employed for stability analysis of polynomial fuzzy control systems under imperfect premise matching of which the fuzzy model and fuzzy controller do not share the same membership functions the solution of the sos based stability conditions can be found numerically using sostools which is a free third party matlab toolbox numerical examples are given to illustrate the effectiveness of the proposed stability conditions