on some results in fuzzy metric spaces abstract we define a hausdorff topology on a fuzzy metric space introduced by kramosil and michalek kybernetica 11 1975 326 334 and prove some known results of metric spaces including baire s theorem for fuzzy metric spaces

dissipativity analysis for singular systems with time varying delays this paper is concerned with the dissipativity analysis problem for singular systems with time varying delays a delay dependent criterion is established to guarantee the dissipativity of the underlying systems using the delay partitioning technique all the results given in this paper are not only dependent upon the time delay but also dependent upon the number of delay partitions the effectiveness and the reduced conservatism of the derived results are demonstrated by two illustrative examples

on some results of analysis for fuzzy metric spaces abstract a necessary and sufficient condition for a fuzzy metric space to be complete is given we prove that a subspace of a separable fuzzy metric space is separable and every separable fuzzy metric space is second countable uniform limit theorem is generalized to fuzzy metric spaces

improved h control of discrete time fuzzy systems a cone complementarity linearization approach in this paper new results are presented for h analysis and synthesis problems of discrete time takagi sugeno ts fuzzy systems by defining a multiple lyapunov function a new sufficient condition guaranteeing the h performance of the ts fuzzy systems is first derived which is expressed by a set of linear matrix inequalities lmis both theoretical analysis and numerical examples show that such a new condition is less conservative than previous results obtained within the quadratic framework based on this new condition for h performance the corresponding h controller design problem is then investigated different from the traditional quadratic framework the synthesis problem is solved by exploiting the cone complementarity linearization ccl method together with a sequential minimization problem subject to lmi constraints obtained for the existence of admissible controllers which can be readily solved by using standard numerical software

compatible coarse nodal and edge elements through energy functionals we propose new algorithms for the setup phase of algebraic multigrid amg solvers for linear systems coming from edge element discretization the construction of coarse levels is performed by solving an optimization problem with a lagrange multiplier method we minimize the energy of coarse bases under a constraint linking coarse nodal and edge element bases on structured meshes the resulting amg method and the geometric multigrid method behave similarly as preconditioners on unstructured meshes the convergence rate of our method compares favorably with the amg method of reitzinger and schoberl

stability and stabilization of a class of fuzzy time delay descriptor systems this paper studies a class of fuzzy time delay descriptor systems in the extended takagi sugeno t s fuzzy model sufficient conditions are derived for the stability and stabilization in terms of linear matrix inequalities lmis illustrative examples are given to show the effectiveness and the advantages of the present results

optimal h filtering in networked control systems with multiple packet dropouts abstract this paper studies the problem of h filtering in networked control systems ncss with multiple packet dropouts a new formulation enables us to assign separate dropout rates from the sensors to the controller and from the controller to the actuators by employing the new formulation random dropout rates are transformed into stochastic parameters in the system s representation a generalized h norm for systems with stochastic parameters and both stochastic and deterministic inputs is derived the stochastic h norm of the filtering error is used as a criterion for filter design in the ncs framework a set of linear matrix inequalities lmis is given to solve the corresponding filter design problem a simulation example supports the theory

h output feedback control of fuzzy system models under sampled measurements this paper studies the problem of control for a class of fuzzy system models by using a linear output controller the system under consideration is described by a continuous time fuzzy system model under sampled output measurements the premise variables of the fuzzy system model are assumed unmeasurable we develop a technique for designing an output feedback control law which globally stabilises this class of fuzzy system models a design algorithm for constructing the linear output controller is given a numerical simulation example is given to show the potential of the proposed techniques

a banach space without a basis which has the bounded approximation property can be approximated by finite rank operators uniformly on compact sets it is clear that xhasabasis xhasbap xhasap the fact that the converse implication to the second one does not hold in general was discovered by figiel and johnson 8 soon after enflo s example 7 of a space without ap the main purpose of this paper is to show that also the implication bap basis does not hold in general this answers problems asked by a number of authors e g 14 18 27 before stating the result we recall more notation for a given basis x n of x one denotes by bc x n the basis constant of ix the smallest k such that

h_ infty fuzzy control with randomly occurring infinite distributed delays and channel fadings in this paper the h output feedback control problem is investigated for a class of discrete time fuzzy systems with randomly occurring infinite distributed delays and channel fadings a random variable obeying the bernoulli distribution is introduced to account for the probabilistic infinite distributed delays the stochastic rice fading model is employed to simultaneously describe the phenomena of random time delays and channel fadings via setting different values of the channel coefficients the aim of this paper is to design an h output feedback fuzzy controller such that the closed loop takagi sugeno t s fuzzy control system is exponentially mean square stable and the disturbance rejection attenuation is constrained to a given level by means of the h performance index intensive analysis is carried out to obtain sufficient conditions for the existence of desired output feedback controllers ensuring both the exponential mean square stability and the prescribed h performance the cone complementarity linearization algorithm is utilized to cast the controller design problem into a sequential minimization one that is solvable by the semi definite programming method a simulation result is exploited to illustrate the usefulness and effectiveness of the proposed design technique

robust h control for a class of nonlinear discrete time delay stochastic systems with missing measurements this paper is concerned with the problem of robust h output feedback control for a class of uncertain discrete time delayed nonlinear stochastic systems with missing measurements the parameter uncertainties enter into all the system matrices the time varying delay is unknown with given low and upper bounds the nonlinearities satisfy the sector conditions and the missing measurements are described by a binary switching sequence that obeys a conditional probability distribution the problem addressed is the design of an output feedback controller such that for all admissible uncertainties the resulting closed loop system is exponentially stable in the mean square for the zero disturbance input and also achieves a prescribed h performance level by using the lyapunov method and stochastic analysis techniques sufficient conditions are first derived to guarantee the existence of the desired controllers and then the controller parameters are characterized in terms of linear matrix inequalities lmis a numerical example is exploited to show the usefulness of the results obtained

technical communique fuzzy h output feedback control of nonlinear systems under sampled measurements this paper studies the problem of designing an h fuzzy feedback control for a class of nonlinear systems described by a continuous time fuzzy system model under sampled output measurements the premise variables of the fuzzy system model are allowed to be unavailable we develop a technique for designing an h fuzzy feedback control that guarantees the l 2 gain from an exogenous input to a controlled output is less than or equal to a prescribed value a design algorithm for constructing the h fuzzy feedback controller is given

adaptive fuzzy output tracking control of mimo nonlinear uncertain systems in this paper the adaptive fuzzy tracking control problem is discussed for a class of uncertain multiple input multiple output mimo nonlinear systems with the block triangular structure the fuzzy logic systems are used to approximate the unknown nonlinear functions by using the backstepping technique the adaptive fuzzy tracking control design scheme is developed which has minimal learning parameterizations the adaptive fuzzy tracking controllers guarantee that the outputs of systems converge to a small neighborhood of the reference signals and all the signals in the closed loop system are semiglobally uniformly ultimately bounded two examples are used to show the effectiveness of the approach

on the topological structure of km fuzzy metric spaces and normed spaces in this paper some relations among the axioms of km fuzzy metric spaces and km fuzzy normed spaces are discussed and some characterizations concerning the additional axiom are given also a quasi metric family and a quasi norm family corresponding respectively to the km fuzzy metric spaces and the km fuzzy normed spaces are introduced and studied using their properties the different topological structures of km fuzzy metric spaces and km fuzzy normed spaces with variable t norm are described and some new properties on these spaces are obtained as their special cases the topological structures and properties concerning gv fuzzy metric spaces and gv fuzzy normed spaces are presented

h sub spl infin fuzzy output feedback control design for nonlinear systems an lmi approach addresses the problem of stabilizing a class of nonlinear systems by using an h sub spl infin fuzzy output feedback controller first a class of nonlinear systems is approximated by a takagi sugeno ts fuzzy model then based on a well known lyapunov functional approach we develop a technique for designing an h sub spl infin fuzzy output feedback control law which guarantees the l sub 2 gain from an exogenous input to a regulated output is less or equal to a prescribed value a design algorithm for constructing an h sub spl infin fuzzy output feedback controller is given in contrast to the existing results the premise variables of the h sub spl infin fuzzy output feedback controller are not necessarily to be the same as the premise variables of the ts fuzzy model of the plant a numerical simulation example is presented to illustrate the theory development

fuzzy bounded linear operators in this paper a notion of boundedness of a linear operator from a fuzzy normed linear space to another fuzzy normed linear space is introduced and two types strong and weak of fuzzy bounded linear operators are defined relation between fuzzy continuity and fuzzy boundedness is studied definitions of fuzzy bounded linear functionals are given and the notions of fuzzy dual spaces are developed the hahn banach theorem the open mapping theorem the closed graph theorem and the uniform boundedness principle theorem are established

robust filter for nonlinear stochastic partial differential systems in sensor signal processing fuzzy approach this study addresses a robust h filter design problem for nonlinear stochastic partial differential systems nspdss with random external disturbance and measurement noise in the spatiotemporal domain for nspdss a robust h filter design through a set of sensor measurements needs to solve a complex second order hamilton jacobi integral inequality hjii in order to simplify the design procedure a fuzzy stochastic partial differential system based on a fuzzy interpolation approach is proposed to approximate the nspds then a fuzzy stochastic spatial state space model is developed to represent the fuzzy stochastic partial differential system via the semidiscretization finite difference scheme and the kronecker product based on this model a robust h filter design is proposed to achieve the robust state estimation via solving linear matrix inequalities lmis instead of a second order hjii the proposed robust fuzzy h filter efficiently attenuates the effect of spatiotemporal external disturbances and measurement noise on the state estimation of nspdss from the area energy point of view finally a robust h state estimation example of heat transfer system is given to illustrate the design procedure and to confirm the h filtering performance of the proposed robust filter design method

brief paper stabilization of markovian jump linear system over networks with random communication delay this paper is concerned with the stabilization problem for a networked control system with markovian characterization we consider the case that the random communication delays exist both in the system state and in the mode signal which are modeled as a markov chain the resulting closed loop system is modeled as a markovian jump linear system with two jumping parameters and a necessary and sufficient condition on the existence of stabilizing controllers is established an iterative linear matrix inequality lmi approach is employed to calculate a mode dependent solution finally a numerical example is given to illustrate the effectiveness of the proposed design method

some properites of fuzzy metric spaces abstract we prove that the topology induced by any complete fuzzy metric space in the sense of george and veeramani is completely metrizable we also show that every separable fuzzy metric space admits a precompact fuzzy metric and that a fuzzy metric space is compact if and only if it is precompact and complete finally we generalize among other classical results the niemytzki tychonoff theorem to fuzzy metric spaces

delay dependent guaranteed cost control for t s fuzzy systems with time delays this study introduces a guaranteed cost control method for nonlinear systems with time delays which can be represented by takagi sugeno t s fuzzy models with time delays the state feedback and generalized dynamic output feedback approaches are considered the generalized dynamic output feedback controller is presented by a new fuzzy controller architecture which is of dual indexed rule base it considers both the dynamic part and the output part of t s fuzzy model which guarantees that the controller without any delay information can stabilize time delay t s fuzzy systems based on delay dependent lyapunov functional approach some sufficient conditions for the existence of state feedback controller are provided via parallel distributed compensation pdc first second the corresponding conditions are extended into the generalized dynamic output feedback closed loop system via so called generalized pdc technique the upper bound of time delay can be obtained using convex optimization such that the system can be stabilized for all time delays whose sizes are not larger than the bound the minimizing method is also proposed to search the suboptimal upper bound of guaranteed cost function the effectiveness of the proposed method can be shown by the simulation examples

approximation properties in fuzzy normed spaces the paper is concerned with approximation properties which are defined in fuzzy normed spaces first we introduce the approximation property and the bounded approximation property next we provide two main examples first example is a fuzzy normed space that does not have the approximation property and second example is a fuzzy normed space with the approximation property that does not have the bounded approximation property finally we provide characterizations of approximation properties in fuzzy normed spaces

stabilization of multi group models with multiple dispersal and stochastic perturbation via feedback control based on discrete time state observations abstract this paper focuses on the multi group models with multiple dispersal and stochastic perturbation mgmds the effect of both multiple dispersal among groups and stochastic perturbation are taken into consideration the stabilization of mgmds is investigated via feedback control based on the discrete time state observations in addition a systematic method is given to construct a global lyapunov function for mgmds by means of graph theory and lyapunov method some sufficient conditions are obtained to ensure the stabilization in the sense of mean square asymptotical stability an upper bound of the duration between two consecutive state observations is estimated moreover to show the applicability of our results the main theory is employed to a stochastic coupled oscillators finally a numerical example is given to illustrate the effectiveness and feasibility of the theoretical results

design of observer based h_ infty control for fuzzy time delay systems this paper addresses the problem of observer based hinfin control for nonlinear systems with time varying delay represented by takagi sugeno t s fuzzy model it presents a single step linear matrix inequality lmi method for the fuzzy control design which overcomes the drawback of the two step lmi approach often encountered in the literature the derivation relies mainly on a proposed matrix decoupling technique using which a resultant matrix inequality can be equivalently converted to strict lmis when restricted to delay free fuzzy systems the present results improve or reduce to existing ones illustrative examples show the effectiveness and merits of the present results

comments on robust stabilization of a class of uncertain nonlinear systems via fuzzy control quadratic stabilizability h sup spl infin control theory and linear matrix inequalities this paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust fuzzy controllers to stabilize the uncertain nonlinear systems first a stability condition for takagi and sugeno s fuzzy model is given in terms of lyapunov stability theory next new stability conditions for a generalized class of uncertain systems are derived from robust control techniques such as quadratic stabilization h sup spl infin control theory and linear matrix inequalities the derived stability conditions are used to analyze the stability of takagi and sugeno s fuzzy control systems with uncertainty which can be regarded as a generalized class of uncertain nonlinear systems the design method employs the so called parallel distributed compensation important issues for the stability analysis and design are remarked finally three design examples of fuzzy controllers for stabilizing nonlinear systems and uncertain nonlinear systems are presented

robust mathscr h _ infty filtering for a class of two dimensional uncertain fuzzy systems with randomly occurring mixed delays this paper is concerned with the robust mathscr h infty filtering problem for a class of 2 d uncertain fuzzy systems with randomly occurring mixed delays romds the underlying 2 d systems are described by the fornasini marchesini model and the uncertainty is expressed in a linear fraction form an improved takagi sugeno t s fuzzy model corresponding to the spatial promise variables is adopted to represent the complicated 2 d nonlinear system the mixed delays consisting of both discrete and distributed delays are allowed to appear in a random manner governed by two sets of bernoulli distributed white sequences with known probability a full order fuzzy filter is constructed to estimate the output signal such that in the presence of parameter uncertainties and romds the dynamics of the estimation errors is asymptotically stable with a prescribed mathscr h infty disturbance attenuation level based on the stochastic analysis technique and the lyapunov like functional sufficient conditions are established to ensure the existence of the desired filters and the explicit expressions of such filters are derived by means of the solution to a class of convex optimization problems that can be solved via standard software packages a numerical example is provided to demonstrate the effectiveness of the developed filter design algorithms and the filter performances with and without fuzzy rules are also compared

schauder bases and approximation property in fuzzy normed spaces our aim in this article is to introduce and study the notion of weak and strong schauder bases in fuzzy normed spaces further we introduce strong and weak fuzzy approximation properties and set a relationship between these two new notions which may provide an acceleration to the structural analysis of fuzzy normed spaces

optimal cal h _ 2 filtering in networked control systems with multiple packet dropout this note studies the problem of optimal h2 filtering in networked control systems ncss with multiple packet dropout a new formulation is employed to model the multiple packet dropout case where the random dropout rate is transformed into a stochastic parameter in the system s representation by generalization of the h2 norm definition new relations for the stochastic norm of a linear discrete time stochastic parameter system represented in the state space form are derived the stochastic h2 norm of the estimation error is used as a criterion for filter design in the ncs framework a set of linear matrix inequalities lmis is given to solve the corresponding filter design problem a simulation example supports the theory

extended dissipative state estimation for markov jump neural networks with unreliable links this paper is concerned with the problem of extended dissipativity based state estimation for discrete time markov jump neural networks nns where the variation of the piecewise time varying transition probabilities of markov chain is subject to a set of switching signals satisfying an average dwell time property the communication links between the nns and the estimator are assumed to be imperfect where the phenomena of signal quantization and data packet dropouts occur simultaneously the aim of this paper is to contribute with a markov switching estimator design method which ensures that the resulting error system is extended stochastically dissipative in the simultaneous presences of packet dropouts and signal quantization stemmed from unreliable communication links sufficient conditions for the solvability of such a problem are established based on the derived conditions an explicit expression of the desired markov switching estimator is presented finally two illustrated examples are given to show the effectiveness of the proposed design method

robust h_ infty fuzzy output feedback control with multiple probabilistic delays and multiple missing measurements in this paper the robust h control problem is investigated for a class of uncertain discrete time fuzzy systems with both multiple probabilistic delays and multiple missing measurements a sequence of random variables all of which are mutually independent but obey the bernoulli distribution is introduced to account for the probabilistic communication delays the measurement missing phenomenon occurs in a random way the missing probability for each sensor satisfies a certain probabilistic distribution in the interval here the attention is focused on the analysis and design of h fuzzy output feedback controllers such that the closed loop takagi sugeno t s fuzzy control system is exponentially stable in the mean square the disturbance rejection attenuation is constrained to a given level by means of the h performance index intensive analysis is carried out to obtain sufficient conditions for the existence of admissible output feedback controllers which ensures the exponential stability as well as the prescribed h performance the cone complementarity linearization procedure is employed to cast the controller design problem into a sequential minimization one that is solved by the semi definite program method simulation results are utilized to demonstrate the effectiveness of the proposed design technique in this paper

fuzzy model based fault tolerant design for nonlinear stochastic systems against simultaneous sensor and actuator faults this paper addresses the problem of fault estimation and fault tolerant control for a class of takagi sugeno t s fuzzy ito stochastic systems subject to simultaneously sensor and actuator faults the main difficulty in this study is that sensor faults actuator faults and stochastic noise that are governed by brownian motion are taken into simultaneous consideration in a unified framework and traditional fault tolerant approaches are not effective to solve this research issue a new descriptor fuzzy sliding mode observer approach is presented in this paper to obtain the simultaneous estimates of system state sensor fault and actuator fault vectors based on the state estimates an observer based fault tolerant control ftc scheme is developed to stabilize the resulting closed loop system finally a simulation example is provided to show the effectiveness of the proposed fault tolerant approach

a novel approach to filter design for t s fuzzy discrete time systems with time varying delay in this paper the problem of l2 l filtering for a class of discrete time takagi sugeno t s fuzzy time varying delay systems is studied our attention is focused on the design of full and reduced order filters that guarantee the filtering error system to be asymptotically stable with a prescribed h performance sufficient conditions for the obtained filtering error system are proposed by applying an input output approach and a two term approximation method which is employed to approximate the time varying delay the corresponding full and reduced order filter design is cast into a convex optimization problem which can be efficiently solved by standard numerical algorithms finally simulation examples are provided to illustrate the effectiveness of the proposed approaches

finite dimensional fuzzy normed linear space abstract the concept of a fuzzy normed linear space is introduced it is proved that in a finite dimensional fuzzy normed linear space fuzzy norms are the same upto fuzzy equivalence finite dimensional fuzzy subspaces of a fuzzy normed linear space are proved to be necessarily complete fuzzy normed linear spaces

fuzzy topological vector spaces ii abstract some of the properties of fuzzy topological vector spaces are investigated also there are given necessary and sufficient conditions for a family of fuzzy sets in a vector space e to be the family of all neighborhoods of zero for a fuzzy linear topology

schauder bases in banach spaces application to numerical solutions of differential equations abstract in this work we present a numerical method for approximating the solution of a linear differential problem we formulate a general problem in a banach space making use of a schauder basis and the tau method to approximate the load function and the solution of the differential problem finally we offer a numerical example

an energy minimizing interpolation for robust multigrid methods we propose a robust interpolation for multigrid based on the concepts of energy minimization and approximation it can handle pde coefficients of various types on structured or unstructured grids under one framework the formulation is general it can be applied to any dimension we demonstrate numerically the effectiveness of the multigrid method in two dimensions by applying it to a discontinuous coefficient problem an oscillatory coefficient problem and an anisotropic problem empirically the convergence rate is independent of the coefficients of the underlying pde in addition to being independent of the mesh size the proposed method is primarily designed for second order elliptic pdes with possible extensions to other classes of problems such as integral equations

optimal full order and reduced order estimators for discrete time systems with multiple packet dropouts this paper is concerned with the estimation problem for discrete time stochastic linear systems with multiple packet dropouts based on a recently developed model for multiple packet dropouts the original system is transferred to a stochastic parameter system by augmentation of the state and measurement the optimal full order linear filter of the form of employing the received outputs at the current and last time instants is investigated the solution to the optimal linear filter is given in terms of a riccati difference equation governed by packet arrival rate the optimal filter is reduced to the standard kalman filter when there are no packet dropouts the steady state filter is also studied a sufficient condition for the existence of the steady state filter is given and the asymptotic stability of the optimal filter is analyzed at last a reduced order filter is investigated

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

delay dependent h control for uncertain fuzzy systems with time varying delays this paper addresses the robust stabilization and robust h control problems of uncertain fuzzy delayed systems via a parallel distributed compensation pdc scheme the uncertainties are norm bounded and the delay may be either constant or time varying and either differentiable or non differentiable presented in this paper are some robust stabilization and robust h control criteria which are delay dependent in general and delay derivative dependent when the delay is differentiable these results enjoy much less conservatism and more computational simplicity compared with those in the existing literature and permit if the delay is differentiable the derivative to be larger than one some examples are given to illustrate the results in this paper

h_ infty fuzzy control of nonlinear systems under unreliable communication links this paper investigates the problem of h infin fuzzy control of nonlinear systems under unreliable communication links the nonlinear plant is represented by a takagi sugeno t s fuzzy model and the control strategy takes the form of parallel distributed compensation the communication links existing between the plant and controller are assumed to be imperfect that is data packet dropouts occur intermittently which appear typically in a network environment and stochastic variables satisfying the bernoulli random binary distribution are utilized to model the unreliable communication links attention is focused on the design of h infin controllers such that the closed loop system is stochastically stable and preserves a guaranteed h infin performance two approaches are developed to solve this problem based on the quadratic lyapunov function and the basis dependent lyapunov function respectively several examples are provided to illustrate the usefulness and applicability of the developed theoretical results

finite time h fuzzy control of nonlinear markovian jump delayed systems with partly uncertain transition descriptions abstract this paper addresses a finite time h fuzzy control problem for a class of nonlinear markovian jump delayed systems with partly uncertain transition descriptions which is represented as a takagi sugeno t s fuzzy model a new homogeneous polynomial of partly uncertain transition rates is chosen free matrix based and double integral forms of the wirtinger based integral inequalities are employed to make the proposed approach less conservative then sufficient conditions are derived such that the fuzzy nonlinear makovian jump delayed system exhibits stochastic finite time boundedness finally two numerical examples are given to illustrate the effectiveness of the proposed design methodology

universal fuzzy models and universal fuzzy controllers for stochastic nonaffine nonlinear systems this paper investigates the universal fuzzy model and universal fuzzy controller problems for stochastic nonaffine nonlinear systems the underlying mechanism of stochastic fuzzy logic is first discussed and a stochastic generalized fuzzy model with new stochastic fuzzy rule base is then given based on their function approximation capability these kinds of stochastic generalized fuzzy models are shown to be universal fuzzy models for stochastic nonaffine nonlinear systems under some sufficient conditions an approach to stabilization controller design for stochastic nonaffine nonlinear systems is then developed through their stochastic generalized takagi sugeno t s fuzzy approximation models then the results of universal fuzzy controllers for two classes of stochastic nonlinear systems along with constructive procedures to obtain the universal fuzzy controllers are also provided respectively finally a numerical example is presented to illustrate the effectiveness of the proposed approach

analysis and synthesis of nonlinear time delay systems via fuzzy control approach takagi sugeno ts fuzzy models 1985 1992 can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input output i o submodels in this paper the ts fuzzy model approach is extended to the stability analysis and control design for both continuous and discrete time nonlinear systems with time delay the ts fuzzy models with time delay are presented and the stability conditions are derived using lyapunov krasovskii approach we also present a stabilization approach for nonlinear time delay systems through fuzzy state feedback and fuzzy observer based controller sufficient conditions for the existence of fuzzy state feedback gain and fuzzy observer gain are derived through the numerical solution of a set of coupled linear matrix inequalities an illustrative example based on the cstr model is given to design a fuzzy controller

a new method for stabilization of networked control systems with random delays we consider the stabilization problem for a class of networked control systems in the discrete time domain with random delays the sensor to controller and controller to actuator delays are modeled as two markov chains and the resulting closed loop systems are jump linear systems with two modes the necessary and sufficient conditions on the existence of stabilizing controllers are established it is shown that state feedback gains are mode dependent an iterative linear matrix inequality lmi approach is employed to calculate the state feedback gains

multigrid in h div and h curl summary we consider the solution of systems of linear algebraic equations which arise from the finite element discretization of variational problems posed in the hilbert spaces bf h div and bf h curl in three dimensions we show that if appropriate finite element spaces and appropriate additive or multiplicative schwarz smoothers are used then the multigrid v cycle is an efficient solver and preconditioner for the discrete operator all results are uniform with respect to the mesh size the number of mesh levels and weights on the two terms in the inner products

fuzzy quasi pseudometrics on algebraic structures abstract in this work we state a number of theorems about fuzzy quasi pseudometrizable algebraic structures our most useful results are 1 a fuzzy semitopological group whose topology is induced by a left invariant fuzzy quasi pseudometric then it is a fuzzy paratopological topological group 2 if the topology on a semigroup s is induced by an invariant fuzzy quasi pseudometric then s is a fuzzy topological semigroup and 3 the same conclusion is valid for a left invariant fuzzy quasi pseudometric on a monoid g such that the left translations are open and the right translations are continuous at the identity e of g by means of the standard fuzzy quasi pseudometric m d associated to a quasi pseudometric d our results apply in the case of semitopological groups semigroups and monoids in order to obtain new results that allow us to generalize and to strengthen previous outcomes

delay dependent robust h sub spl infin control for t s fuzzy systems with time delay this paper focuses on the problem of delay dependent robust fuzzy control for a class of nonlinear delay systems via state feedback the takagi sugeno t s fuzzy model is adopted for representing a nonlinear system with time delayed state a delay dependent stabilization criterion is first presented then the methods of robust stabilization and robust h sub spl infin control are developed which are dependent on the size of the delay and are based on the solutions of linear matrix inequalities lmis finally a design example of robust h sub spl infin controller for uncertain nonlinear systems is given to illustrate the effectiveness of the approaches proposed in this paper

new results on a delay derivative dependent fuzzy h infty filter design for t s fuzzy systems this paper focuses on the fuzzy h filter design problem for takagi sugeno t s fuzzy systems with interval time varying delays two cases of the time varying delays are considered 1 the delays are differentiable and have both the lower and upper bounds of the delay derivatives and 2 the delays are bounded but not necessary to be differentiable since we employ a new fuzzy lyapunov krasovskii functional lkf and estimate a tighter upper bound of its derivative the proposed delay derivative dependent bound real lemma brl condition has advantages over some previous results in that it enlarges the application scope but has less conservatism which is established theoretically the brl condition that depends on both the upper and lower bounds of the delay derivatives is derived then based on the aforesaid brl a new fuzzy h filter scheme is proposed and a sufficient condition for the existence of such a filter is established in terms of linear matrix inequalities lmis finally some numerical examples and an application to the truck trailer system are utilized to demonstrate the effectiveness and reduced conservatism of our results

toward an h independent algebraic multigrid method for maxwell s equations we propose a new algebraic multigrid amg method for solving the eddy current approximations to maxwell s equations this amg method has its roots in an algorithm proposed by reitzinger and schoberl the main focus in the reitzinger and schoberl method is to maintain null space properties of the weak nabla times nabla times operator on coarse grids while these null space properties are critical they are not enough to guarantee h independent convergence rates of the overall multigrid scheme we present a new strategy for choosing intergrid transfers that not only maintains the important null space properties on coarse grids but also yields significantly improved multigrid convergence rates this improvement is related to those we explored in a previous paper but is fundamentally simpler easier to compute and performs better with respect to both multigrid operator complexity and convergence rates the new strategy builds on ideas in smoothed aggregation to improve the approximation property of an existing interpolation operator by carefully choosing the smoothing operators we show how it is sometimes possible to achieve h independent convergence rates with a modest increase in multigrid operator complexity though this ideal case is not always possible the overall algorithm performs significantly better than the original scheme in both iterations and run time finally the reitzinger and schoberl method as well as our previous smoothed method are shown to be special cases of this new algorithm

h sub spl infin control for networked systems with random communication delays this note is concerned with a new controller design problem for networked systems with random communication delays two kinds of random delays are simultaneously considered i from the controller to the plant and ii from the sensor to the controller via a limited bandwidth communication channel the random delays are modeled as a linear function of the stochastic variable satisfying bernoulli random binary distribution the observer based controller is designed to exponentially stabilize the networked system in the sense of mean square and also achieve the prescribed h sub spl infin disturbance attenuation level the addressed controller design problem is transformed to an auxiliary convex optimization problem which can be solved by a linear matrix inequality lmi approach an illustrative example is provided to show the applicability of the proposed method

h2 guaranteed cost fuzzy control for uncertain nonlinear systems via linear matrix inequalities abstract this paper deals with h2 guaranteed cost gc fuzzy control problem for uncertain continuous time nonlinear systems the state feedback case and observer based output feedback case are considered the takagi and sugeno t s fuzzy model is employed to represent a nonlinear system with parametric uncertainties sufficient conditions for the existence of h2 gc fuzzy controllers are given in terms of linear matrix inequalities lmis the suboptimal h2 gc fuzzy controllers are given by means of the lmi optimization procedures which cannot only guarantee that the closed loop overall fuzzy systems are globally asymptotically stable but also provide an optimized upper bound on the quadratic performance cost finally an example is presented to illustrate the effectiveness of the proposed fuzzy controllers

pinning synchronization in t s fuzzy complex networks with partial and discrete time couplings communication constraints which may lead to the degradation of performance are common and unavoidable in a real world network in this paper two kinds of communication constraints are considered during the process of information transmission in takagi sugeno ts fuzzy complex network 1 partial couplings where only some part of nodes state information can be transmitted and the channel matrices are introduced to reflect such a phenomenon and 2 discrete time couplings where the nodes information are sampled at certain time instants this is the first time when both communication constraints are simultaneously considered in fuzzy complex networks compared with the perfect communication much less information is available for synchronization to overcome this difficulty a regrouping method is employed to reconstruct the fuzzy network the concise conditions are then proposed to ensure pinning synchronization of fuzzy complex networks with partial and discrete time couplings simulation examples are also provided to demonstrate the effectiveness of the theoretical results

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 improved algebraic multigrid method for solving maxwell s equations we propose two improvements to the reitzinger and schoberl algebraic multigrid amg method for solving the eddy current approximations to maxwell s equations the main focus in the reitzinger schoberl method is to maintain null space properties of the weak nabla times nabla times operator on coarse grids while these null space properties are critical they are not enough to guarantee h independent convergence of the overall multigrid method we illustrate how the reitzinger schoberl amg method loses h independence due to the somewhat limited approximation property of the grid transfer operators we present two improvements to these operators that not only maintain the important null space properties on coarse grids but also yield significantly improved multigrid convergence rates the first improvement is based on smoothing the reitzinger schoberl grid transfer operators the second improvement is obtained by using higher order nodal interpolation to derive the corresponding amg interpolation operators while not completely h independent the resulting amg cg method demonstrates improved convergence behavior while maintaining low operator complexity

reliable h_ infty control for discrete time fuzzy systems with infinite distributed delay in this paper the problem of reliable h control is investigated for discrete time takagi sugeno t s fuzzy systems with infinite distributed delay and actuator faults a discrete time homogeneous markov chain is used to represent the stochastic behavior of actuator faults in terms of a stochastic fuzzy lyapunov functional a sufficient condition is proposed to ensure that the resultant closed loop system is exponentially stable in the mean square sense with an h performance index based on the derived condition the reliable h control problem is solved and an explicit expression of the desired controller is also given the case of no failure in the actuator is also considered a numerical example is given to demonstrate that our results are effective and less conservative

exact de rham sequences of spaces defined on macro elements in two and three spatial dimensions this paper proposes new finite element spaces that can be constructed for agglomerates of standard elements that have certain regular structure the main requirement is that the agglomerates share faces that have closed boundaries composed of 1 d edges the spaces resulting from the agglomerated elements are subspaces of the original de rham sequence of h 1 conforming h mathbf curl conforming h mathbf div conforming and piecewise constant spaces associated with an unstructured fine mesh the procedure can be recursively applied so that a sequence of nested de rham complexes can be constructed as an illustration we generate coarser spaces from the sequence corresponding to the lowest order nedelec spaces lowest order raviart thomas spaces and for piecewise linear h 1 conforming spaces all in three dimensions the resulting v cycle multigrid methods used in preconditioned conjugate gradient iterations appear to perform similar to those of the geometrically refined case

generalized h2 fault detection for two dimensional markovian jump systems this paper is concerned with the generalized h 2 fault detection for two dimensional 2 d discrete time markovian jump systems the mathematical model of the 2 d system is established upon the well known roesser model and the measurement missing phenomenon which appears typically in a network environment is modeled by a stochastic variable satisfying the bernoulli random binary distribution in addition the transition probabilities of the markovian jump process are assumed to be partly accessed that is the transition probabilities are partly known our attention is focused on the design of a fault detection filter or a residual generation system which guarantees the fault detection system to be mean square asymptotically stable and to have a prescribed generalized h 2 performance sufficient conditions for the existence of a desired fault detection filter are established in terms of linear matrix inequalities lmis a numerical example is provided to illustrate the effectiveness of the proposed design method

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