parameter dependent lmis in robust analysis characterization of homogeneous polynomially parameter dependent solutions via lmi relaxations this note investigates the robust stability of uncertain linear time invariant systems in polytopic domains by means of parameter dependent linear matrix inequality pd lmi conditions exploiting some algebraic properties provided by the uncertainty representation a systematic procedure to construct a family of finite dimensional lmi relaxations is provided the robust stability is assessed by means of the existence of a lyapunov function more specifically a homogeneous polynomially parameter dependent lyapunov hppdl function of arbitrary degree for a given degree if an hppdl solution exists a sequence of relaxations based on real algebraic properties provides sufficient lmi conditions of increasing precision and constant number of decision variables for the existence of an hppdl function which tend to the necessity alternatively if an hppdl solution of degree exists a sequence of relaxations which increases the number of variables and the number of lmis will provide an hppdl solution of larger degree the method proposed can be applied to determine homogeneous parameter dependent matrix solutions to a wide variety of pd lmis by transforming the infinite dimensional lmi problem described in terms of uncertain parameters belonging to the unit simplex in a sequence of finite dimensional lmi conditions which converges to the necessary conditions for the existence of a homogeneous polynomially parameter dependent solution of arbitrary degree illustrative examples show the efficacy of the proposed conditions when compared with other methods from the literature

representations of kac moody and virasoro algebras on modules of greenberg mohapatra algebras the theory of greenberg mohapatra algebras is developed in continuation to a previous paper standard cyclic modules are constructed for the algebras and on them kac moody and virasoro algebras are represented through a basic procedure the representations of kac moody and virasoro algebras help to understand the structure of greenberg mohapatra algebras and the question of possible violation of the pauli exclusion principle

nonquadratic stabilization of continuous t s fuzzy models lmi solution for a local approach this paper is concerned with nonquadratic stabilization design problem for continuous time nonlinear models in the takagi sugeno t s form obtained by sector nonlinearity approach most of the previous results found in the literature intended to establish global nonquadratic stabilization conditions which are hard to uphold due to the difficulty of handling time derivatives of the membership function by changing the paradigm of global stabilization for something less restrictive a local solution to overcome infeasible quadratic stabilization conditions is offered in this paper it is shown that the derived local nonquadratic conditions actually lead to reasonable advantages over the existing quadratic approach as well as some previous nonquadratic attempts moreover conditions for the solvability of state feedback controller design given here are written in the form of linear matrix inequalities lmis which can be efficiently solved by convex optimization techniques simulation examples are given to demonstrate the validity and applicability of the proposed approaches

nonquadratic stabilization conditions for a class of uncertain nonlinear discrete time ts fuzzy models a new approach the discrete time uncertain nonlinear models are considered in a takagi sugeno form and their stabilization is studied through a non quadratic lyapunov function the classical conditions consider a one sample variation here the main results are obtained considering k samples variation i e deltak v x t v x t k v x t the results are shown to always include the classical cases and several examples illustrate the effectiveness of the approach

temperature states on loop groups boson fermion correspondence and a determinant identity the boson fermion correspondence for the representation of the car algebra over l2 s1 c defined by the kms state with chemical potential is considered and the non bijectivity shown using an alternative formulation the correlations are recalculated leading to a determinant identity reminiscent of szego s theorem

spin and wedge representations of infinite dimensional lie algebras and groups abstract we suggest a purely algebraic construction of the spin representation of an infinite dimensional orthogonal lie algebra sections 1 and 2 and a corresponding group section 4 from this we deduce a construction of all level one highest weight representations of orthogonal affine lie algebras in terms of creation and annihilation operators on an infinite dimensional grassmann algebra section 3 we also give a similar construction of the level one representations of the general linear affine lie algebra in an infinite dimensional wedge space along these lines we construct the corresponding representations of the universal central extension of the group sln k t t 1 in spaces of sections of line bundles over infinite dimensional homogeneous spaces section 5

new relaxed stability and stabilization conditions for continuous time t s fuzzy models this paper deals with the problems of stability and stabilization for continuous time takagi sugeno t s models by employing the order relation information of the membership functions mfs the transformation matrix and the pseudo mf vector are obtained the conventional continuous time t s fuzzy model is then transformed to a new compact t s model based on which relaxed stability and stabilization conditions are derived in the form of linear matrix inequalities an improved approach to constructing the transformation matrix is presented which could take full advantage of the order relation information of the mfs and further reduce the conservatism numerical examples are provided 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

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

fuzzy control design of nonlinear systems under unreliable communication links in this study we propose a systematic homogenous polynomial approach for fuzzy control design of discrete time takagi sugeno fuzzy systems under unreliable communication links a novel delayed fuzzy control scheme which is homogenous polynomially parameter dependent on both the current normalized fuzzy weighting function and the one step past normalized fuzzy weighting function is designed to accomplish the assignment of relaxed control synthesis in contrast to the existing methods the closed loop controlled system is stochastically stable in the mean square sense with less conservative stabilization conditions finally simulation results are provided to verify the advantage and the effectiveness of the proposed approach

vertex operators arising from jacobi trudi identities we give an interpretation of the boson fermion correspondence as a direct consequence of the jacobi trudi identity this viewpoint enables us to construct from a generalized version of the jacobi trudi identity the action of a clifford algebra on the polynomial algebras that arrive as analogues of the algebra of symmetric functions a generalized giambelli identity is also proved to follow from that identity as applications we obtain explicit formulas for vertex operators corresponding to characters of the classical lie algebras shifted schur functions and generalized schur symmetric functions associated to linear recurrence relations

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

two dimensional generalized toda lattice the zero curvature representation is obtained for the two dimensional generalized toda lattices connected with semisimple lie algebras the reduction group and conservation laws are found and the mass spectrum is calculated

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

h sub spl infin controller synthesis of fuzzy dynamic systems based on piecewise lyapunov functions and bilinear matrix inequalities this work presents an h sub spl infin controller design method for fuzzy dynamic systems based on techniques of piecewise smooth lyapunov functions and bilinear matrix inequalities it is shown that a piecewise continuous lyapunov function can be used to establish the global stability with h sub spl infin performance of the resulting closed loop fuzzy control systems and the control laws can be obtained by solving a set of bilinear matrix inequalities bmis two examples are given to illustrate the application of the proposed methods

network based h control for t s fuzzy systems with an adaptive event triggered communication scheme abstract this paper extends the prior work of discrete event triggered communication for networked t s fuzzy systems where the next communication instant is determined by an event triggered communication scheme with a constant threshold and the premises of t s fuzzy systems and parallel distribution compensation pdc fuzzy control rules are synchronous firstly an adaptive event triggered communication scheme for ncss is presented which relaxes the assumption of the prior work that the threshold of event triggered communication scheme is a preselected constant secondly an asynchronous premise re construct method for networked t s fuzzy systems is proposed which relaxes the assumption of the prior work that the premises of the plant and the pdc control rules are synchronous we show that the number of transmitted packets generated by the proposed scheme is smaller than those generated by some existing ones while ensuring the desired control performance simulations show the effectiveness of the proposed method

vector generation functions q spectral functions of hyperbolic geometry and vertex operators for quantum affine algebras we investigate the concept of q replicated argument in symmetric functions with its connection to spectral functions of hyperbolic geometry this construction suffices for vector generation functions in the form of q series and string theory we hope that the mathematical side of the construction can be enriched by ideas coming from physics

two constructions of affine lie algebra representations and boson fermion correspondence in quantum field theory we establish an isomorphism between the vertex and spinor representations of affine lie algebras for types dl 1 and dl 1 2 we also study decomposition of spinor representations using the infinite family of casimir operators and prove that they are either irreducible or have two irreducible components we show that the vertex and spinor constructions of the representations can be reformulated in the language of two dimensional quantum field theory in this physical context the two constructions yield the generalized sine gordon and thirring models respectively already in renormalized form the isomorphism of representations implies an equivalence of these two models which is known in quantum field theory as the boson fermion correspondence

dynamic output feedback predictive control of a takagi sugeno model with bounded disturbance this paper considers predictive control of a takagi sugeno fuzzy model with bounded disturbance strictly satisfying the input and state constraints the membership function dependent dynamic output feedback law as in a previous work is utilized the novelty lies in the following technical improvements for the notion of quadratic boundedness which specifies closed loop stability and invariance properties the full lyapunov matrix is utilized the real time ellipsoidal bound of true state is recursively optimized by invoking the s procedure some relaxation scalars being optimized by the norm bounding technique are introduced for better handling the input and state constraints the multistep approach where a sequence of dynamic output feedback laws are optimized at each sampling instant is given to improve the single step approach numerical examples are given to illustrate the effectiveness of the proposed controllers

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

novel stability conditions for discrete time t s fuzzy systems this paper is concerned with the issue of developing a novel strategy to reduce the conservatism of stability conditions for discrete time takagi sugeno t s fuzzy systems unlike the previous ones which are almost quadratic with respect to the state vector a new class of lyapunov functions is proposed which is quadratic with respect to the kronecker products of the state vector thus including almost the existing ones found in the literature as special cases by combining the characterizations of homogeneous matrix polynomials and the properties of membership functions relaxed stability conditions are derived in the form of linear matrix inequalities which can be efficiently solved by the convex optimization techniques finally a numerical example is provided to illustrate the effectiveness of the proposed approach

technical communique further studies on lmi based relaxed stabilization conditions for nonlinear systems in takagi sugeno s form this paper further studies stabilization of nonlinear systems represented by a takagi sugeno t s discrete fuzzy model by extending a nonquadratic lyapunov function and applying a nonparallel distributed compensation non pdc law a new stabilization conclusion is presented that is a generalization of some previous results in the literature the new conclusion under a special situation is also suitable for a pdc law which presents to be more relaxed than some existing results an example is provided to demonstrate the effectiveness of the new conclusions

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

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

quantized feedback fuzzy sliding mode control design via memory based strategy this paper is concerned with the sliding mode control smc design for a class of takagi sugeno t s fuzzy nonlinear systems subject to model uncertainties and input quantization mismatch a novel memory based sliding surface is presented which includes not only the current states but also the past state information of the systems sufficient conditions for the design of the switching gains are given via linear matrix inequality lmi technique and then the reaching conditions of the sliding surface is constructed to ensure the reachability of the sliding manifold furthermore an adaptive neuro fuzzy inference system anfis is introduced for reducing the high frequency chattering induced by the signum function term in the sliding mode control the effectiveness of the proposed methodology is illustrated by matlab simulations

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

multi instant observer design of discrete time fuzzy systems a ranking based switching approach this paper generalizes recent results on multi instant observer design for discrete time takagi sugeno fuzzy systems through a valid ranking based switching approach the approach hereby develops a concentrated subdivision of spanning space composed of normalized fuzzy weighting functions and then substantially produces a new ranking based switching mechanism by taking advantage of this ranking based switching mechanism a class of new fuzzy multi instant observers are achieved and more relaxed design conditions with respect to the recent work can be obtained for ensuring the asymptotically stability of the developed state estimation error system two illustrative examples are provided to validate the effectiveness of the result given in this study

control law proposition for the stabilization of discrete takagi sugeno models this paper deals with the stabilization of a class of discrete nonlinear models namely those in the takagi sugeno form its main goal is to reduce conservatism of existing stabilization conditions using a special class of candidate lyapunov functions and an enhanced control law it is shown that the use of the aforementioned lyapunov function leads to less pessimistic solutions the usefulness of the new control law is shown through several examples

generalized symplectic schur functions and suc hierarchy in this paper we first define a generalization of the symplectic schur functions and their vertex operator realizations by means of the vertex operators we obtain a series of non linear partial differential equations of infinite order the symplectic uc hierarchy called the suc hierarchy we regard it as an extension of the symplectic kp hierarchy

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

average dimension of fixed point spaces with applications abstract let g be a finite group f a field and v a finite dimensional fg module such that g has no trivial composition factor on v then the arithmetic average dimension of the fixed point spaces of elements of g on v is at most 1 p dim v where p is the smallest prime divisor of the order of g this answers and generalizes a 1966 conjecture of neumann which also appeared in a paper of neumann and vaughan lee and also as a problem in the kourovka notebook posted by vaughan lee our result also generalizes a recent theorem of isaacs keller meierfrankenfeld and moreto we also classify precisely when equality can occur various applications are given for example another conjecture of neumann and vaughan lee is proven and some results of segal and shalev are improved and or generalized concerning bfc groups

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

fuzzy basis functions universal approximation and orthogonal least squares learning fuzzy systems are represented as series expansions of fuzzy basis functions which are algebraic superpositions of fuzzy membership functions using the stone weierstrass theorem it is proved that linear combinations of the fuzzy basis functions are capable of uniformly approximating any real continuous function on a compact set to arbitrary accuracy based on the fuzzy basis function representations an orthogonal least squares ols learning algorithm is developed for designing fuzzy systems based on given input output pairs then the ols algorithm is used to select significant fuzzy basis functions which are used to construct the final fuzzy system the fuzzy basis function expansion is used to approximate a controller for the nonlinear ball and beam system and the simulation results show that the control performance is improved by incorporating some common sense fuzzy control rules

local stabilization for continuous time takagi sugeno fuzzy systems with time delay this brief paper investigates the local stabilization for continues time takagi sugeno fuzzy systems with constant time delay in order to deal with the time delay we design a lyapunov krasovskii functional that is dependent on the membership function based on the lyapunov krasovskii functional and the analysis of the time derivative of the membership function less conservative results can be obtained however the lyapunov krasovskii functional is designed so complicated that the lyapunov level set is hard to be measured directly alternatively two sets are obtained to estimate the local stabilization one set is for the time varying initial conditions and the other is for the time invariant initial conditions the relationship between the two sets are also discussed in the end two examples are given to illustrate the effectiveness of the proposed approach

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

a note on the boson fermion correspondence and infinite dimensional groups we show how to construct irreducible projective representations of the infinite dimensional lie group map s1 mathbb t by embedding it into the group of bogoliubov automorphisms of the car using techniques of g segal for extending certain representations of map s1 su 2 we show that our representations extend to give representations of a certain infinite dimensional superalgebra we relate our work to the well known boson fermion correspondence which exists in 1 1 dimensions

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

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

further studies on control synthesis of discrete time t s fuzzy systems via useful matrix equalities this paper is concerned with further studies on the control synthesis of discrete time nonlinear systems in the takagi sugeno t s fuzzy form to do this a novel slack variable technique is presented by developing some useful matrix equalities which are homogenous polynomially parameter dependent on both the current time normalized fuzzy weighting functions and the past time normalized fuzzy weighting functions under the framework of homogenous matrix polynomials the algebraic properties of both the current time normalized fuzzy weighting functions and the past time normalized fuzzy weighting functions are collected for the first time into sets of united collection matrices consequently the relaxation quality of control synthesis of discrete time t s fuzzy systems is improved i e the convergence of asymptotically necessary and sufficient stabilization conditions is further sped up finally a numerical example is provided to illustrate the effectiveness of the proposed result

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

controller synthesis of fuzzy dynamic systems based on piecewise lyapunov functions this paper presents a kind of controller synthesis method for fuzzy dynamic systems based on a piecewise smooth lyapunov function the basic idea of the proposed approach is to construct controllers for the fuzzy dynamic systems in such a way that a piecewise continuous lyapunov function can be used to establish the global stability with h sub spl infin performance of the resulting closed loop fuzzy control systems it is shown that the control laws can be obtained by solving a set of linear matrix inequalities that is numerically feasible with commercially available software an example is given to illustrate the application of the proposed methods

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