stability analysis and synthesis of nonlinear time delay systems via linear takagi sugeno fuzzy models abstract this paper concerns with the stability analysis and synthesis of nonlinear retarded systems via linear takagi sugeno ts fuzzy model approach first the ts fuzzy models with time delay are present and the stability conditions are derived using lyapunov razumikhin functional approach then a stabilization approach for nonlinear retarded systems through fuzzy state feedback and fuzzy observer based controller is proposed it shows that the analysis results provide an efficient technique for the design of fuzzy controllers sufficient conditions for the existence of fuzzy state feedback gain and fuzzy observer gain of the time delay systems are derived through the numerical solution of a set of coupled linear matrix inequalities

finite time asynchronous h control for markov jump repeated scalar non linear systems with input constraints finite time control issue for a quite comprehensive class of system model that is markov jump repeated scalar nonlinear systems mjrsnss has been addressed an asynchronous controller is first proposed in mjrsnss which has less conservatism than mode dependent when the partly available mode information is encountered the input constraints associated with physical limitations in some practical applications have been fully considered which make our model more realistic this paper is concerned with the problem of finite time h control for markov jump repeated scalar nonlinear systems mjrsnss with input constraints the jumps between mjrsnss and desired mode dependent controllers are considered to be nonsynchronous the mode transition of the controllers is governed by a nonstationary markov chain which can model the different degrees of asynchronous jumps between mjrsnss and controllers with the aid of lyapunov krasovskii methodology some h performance criteria for the mjrsnss are proposed based on these criteria sufficient conditions on the existence of the desired controllers are established and then the gains of the controllers can be obtained by solving a convex optimization problem finally an example is presented to illustrate the effectiveness of our method

generalized besicovitch spaces and applications to deterministic homogenization the purpose of the present work is to introduce a framework which enables us to study nonlinear homogenization problems the starting point is the theory of algebras with mean value very often in physics from very simple experimental data one gets complicated structure phenomena these phenomena are represented by functions which are permanent in mean but complicated in detail in addition the functions are subject to the verification of a functional equation which in general is nonlinear the problem is therefore to give an interpretation of these phenomena using functions having the following qualitative properties they are functions that represent a phenomenon on a large scale and which vary irregularly undergoing nonperiodic oscillations on a fine scale in this work we study the qualitative properties of spaces of such functions which we call generalized besicovitch spaces and we prove general compactness results related to these spaces we then apply these results in order to study some new homogenization problems one important achievement of this work is the resolution of the generalized weakly almost periodic homogenization problem for a nonlinear pseudo monotone parabolic type operator we also give the answer to the question raised by frid and silva in their paper 35 h frid j silva homogenization of nonlinear pde s in the fourier stieltjes algebras siam j math anal 41 4 2009 1589 1620 as regards whether there exist or do not exist ergodic algebras that are not subalgebras of the fourier stieltjes algebra

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

h_ bm infty fuzzy control for systems with repeated scalar nonlinearities and random packet losses this paper is concerned with the h infin fuzzy control problem for a class of systems with repeated scalar nonlinearities and random packet losses a modified takagi sugeno t s fuzzy model is proposed in which the consequent parts are composed of a set of discrete time state equations containing a repeated scalar nonlinearity such a model can describe some well known nonlinear systems such as recurrent neural networks the measurement transmission between the plant and controller is assumed to be imperfect and a stochastic variable satisfying the bernoulli random binary distribution is utilized to represent the phenomenon of random packet losses attention is focused on the analysis and design of h infin fuzzy controllers with the same repeated scalar nonlinearities such that the closed loop t s fuzzy control system is stochastically stable and preserves a guaranteed h infin performance sufficient conditions are obtained for the existence of admissible controllers and the cone complementarity linearization procedure is employed to cast the controller design problem into a sequential minimization one subject to linear matrix inequalities which can be readily solved by using standard numerical software two examples are given to illustrate the effectiveness of the proposed design method

a lyapunov like characterization of asymptotic controllability it is shown that a control system in bf r n is asymptotically controllable to the origin if and only if there exists a positive definite continuous functional of the states whose derivative can be made negative by appropriate choices of controls

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

adaptive output feedback control for nonlinear time delay systems by fuzzy approximation approach in this paper the problem of adaptive fuzzy tracking control via output feedback for a class of uncertain single input single output siso strict feedback nonlinear systems with unknown time delay functions is investigated dynamic surface control technique is used to avoid the problem of explosion of complexity which is caused by repeated differentiation of certain nonlinear functions in the backstepping design process in addition the fuzzy logic systems are utilized to approximate the unknown and desired control input signals directly instead of the unknown nonlinear functions the designed controller can guarantee all the signals in the closed loop system to be semiglobally uniformly ultimately bounded and the tracking error to converge to a small neighborhood of the origin simulations results are provided to demonstrate the effectiveness of the proposed methods

deterministic homogenization of non linear non monotone degenerate elliptic operators deterministic homogenization has been till now applied to the study of monotone operators the determination of the limiting problem being systematically based on the monotonicity of the operator under consideration here we mean to show that deterministic homogenization also tackle non monotone operators more precisely under an abstract general hypothesis we study the homogenization of non linear non monotone degenerate elliptic operators we obtain some general homogenization result which result is applied to the resolution of several concrete homogenization problems such as the periodic homogenization and the almost periodic homogenization problems our main tool is the theory of homogenization structures

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

further results for systems with repeated scalar nonlinearities a class of nonlinear systems described by a discrete time state equation containing a repeated scalar nonlinearity is considered this paper sharpens several previous results on the performance synthesis and model reduction for such systems extensions to the case that the nonlinearity is not an odd function are also discussed

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

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

σ convergence of nonlinear parabolic operators abstract we discuss the nonstochastic homogenization of nonlinear parabolic differential operators in an abstract setting framed to bridge the gap between periodic and stochastic homogenization theories instead of the classical periodicity hypothesis we have here an abstract assumption covering a great variety of concrete behaviours in both space and time variables such as the periodicity the almost periodicity the convergence at infinity and others our basic approach is the convergence method generalizing the well known two scale convergence technique fundamental homogenization theorems are proved and several concrete examples are worked out which reveal that homogenization beyond the periodic setting may involve difficulties that are beyond imagination

asynchronous output feedback control of networked nonlinear systems with multiple packet dropouts t s fuzzy affine model based approach this paper investigates the problem of robust output feedback control for a class of networked nonlinear systems with multiple packet dropouts the nonlinear plant is represented by takagi sugeno t s fuzzy affine dynamic models with norm bounded uncertainties and stochastic variables that satisfy the bernoulli random binary distribution are adopted to characterize the data missing phenomenon the objective is to design an admissible output feedback controller that guarantees the stochastic stability of the resulting closed loop system with a prescribed disturbance attenuation level it is assumed that the plant premise variables which are often the state variables or their functions are not measurable so that the controller implementation with state space partition may not be synchronous with the state trajectories of the plant based on a piecewise quadratic lyapunov function combined with an s procedure and some matrix inequality convexifying techniques two different approaches to robust output feedback controller design are developed for the underlying t s fuzzy affine systems with unreliable communication links the solutions to the problem are formulated in the form of linear matrix inequalities lmis finally simulation examples are provided to illustrate the effectiveness of the proposed approaches

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

stabilization with discounted optimal control abstract we provide a condition under which infinite horizon discounted optimal control problems can be used in order to obtain stabilizing controls for nonlinear systems the paper gives a mathematical analysis of the problem as well as an illustration by a numerical example

stabilization of strictly dissipative discrete time systems with discounted optimal control abstract we consider stabilization of an equilibrium point via infinite horizon discounted optimal control in discrete time in addition to applications in economics and social sciences discounted optimal control is a commonly used numerical technique guaranteeing solvability of certain classes of optimal control problems in this paper we present conditions based on strict dissipativity that ensure that the optimally controlled system is asymptotically stable or practically asymptotically stable these conditions are shown to be complementary to recently proposed conditions based on a detectability property illustrative examples are provided

analysis and design of unconstrained nonlinear mpc schemes for finite and infinite dimensional systems we present a technique for computing stability and performance bounds for unconstrained nonlinear model predictive control mpc schemes the technique relies on controllability properties of the system under consideration and the computation can be formulated as an optimization problem whose complexity is independent of the state space dimension based on the insight obtained from the numerical solution of this problem we derive design guidelines for nonlinear mpc schemes which guarantee stability of the closed loop for small optimization horizons these guidelines are illustrated by a finite and an infinite dimensional example

bounds of the induced norm and model reduction errors for systems with repeated scalar nonlinearities the class of nonlinear systems described by a discrete time state equation containing a repeated scalar nonlinearity as in recurrent neural networks is considered sufficient conditions are derived for the stability and induced norm of such systems using positive definite diagonally dominant lyapunov functions or storage functions satisfying appropriate linear matrix inequalities results are also presented for model reduction errors for such systems

on the stability of receding horizon control with a general terminal cost we study the stability and region of attraction properties of a family of receding horizon schemes for nonlinear systems using dini s theorem on the uniform convergence of functions we show that there is always a finite horizon for which the corresponding receding horizon scheme is stabilizing without the use of a terminal cost or terminal constraints after showing that optimal infinite horizon trajectories possess a uniform convergence property we show that exponential stability may also be obtained with a sufficient horizon when an upper bound on the infinite horizon cost is used as terminal cost combining these important cases together with a sandwiching argument we are able to conclude that exponential stability is obtained for input constrained receding horizon schemes with a general nonnegative terminal cost for sufficiently long horizons region of attraction estimates are also included in each of the results

nonstationary l2 l filtering for markov switching repeated scalar nonlinear systems with randomly occurring nonlinearities abstract this paper is concerned with nonstationary l 2 l filtering for markov switching repeated scalar nonlinear systems msrsnss with randomly occurring nonlinearities rons where measurement output is modeled by a mode dependent random variable that satisfying bernouli distribution the new relationship are proposed to depict multiple mutually independent markov chains between original mmsrsnss and nonstationary filters by constructing a proper lyapnov function the msrsnss is stochastically stable with l 2 l performance level is guaranteed accordingly the nonstationary filters are designed where filters are characterised by a two layer structure the paper provides a numerical example verifying the efficacy of established technique

event triggered h control for networked discrete time markov jump systems with repeated scalar nonlinearities this paper investigates the event triggered h control problem for networked discrete time markov jump systems subject to repeated scalar nonlinearities an event triggered communication transmission scheme is adopted and an event generator is presented between the controller and sensor our aim is to design a controller such that although the unavoidable phenomenon of network induced delays is fully considered the resulting closed loop system is stochastically stable with a prescribed h performance level by employing a diagonally dominant type lyapunov functional a co design method is established for the existence of an admissible controller and some available mode dependent event triggered parameters finally the effectiveness of our proposed control design method is shown by a numerical example

h_ bm infty fuzzy filtering of nonlinear systems with intermittent measurements this paper is concerned with the problem of h infin fuzzy filtering of nonlinear systems with intermittent measurements the nonlinear plant is represented by a takagi sugeno t s fuzzy model the measurements transmission from the plant to the filter is assumed to be imperfect and a stochastic variable satisfying the bernoulli random binary distribution is utilized to model the phenomenon of the missing measurements attention is focused on the design of an h infin filter such that the filter error system is stochastically stable and preserves a guaranteed h infin performance a basis dependent lyapunov function approach is developed to design the h infin filter by introducing some slack matrix variables the coupling between the lyapunov matrix and the system matrices is eliminated which greatly facilitates the filter design procedure the developed theoretical results are in the form of linear matrix inequalities lmis finally an illustrative example is provided to show the effectiveness of the proposed approach

multiscale young measures in homogenization of continuous stationary processes in compact spaces and applications abstract we introduce a framework for the study of nonlinear homogenization problems in the setting of stationary continuous processes in compact spaces the latter are functions f t r n q q with f t x f t x where q is a compact hausdorff topological space f c q and t x q q x r n is an n dimensional continuous dynamical system endowed with an invariant radon probability measure it can be easily shown that for almost all q the realization f t x belongs to an algebra with mean value that is an algebra of functions in buc r n containing all translates of its elements and such that each of its elements possesses a mean value this notion was introduced by zhikov and krivenko v v zhikov e v krivenko homogenization of singularly perturbed elliptic operators mat zametki 33 1983 571 582 english transl in math notes 33 1983 294 300 we then establish the existence of multiscale young measures in the setting of algebras with mean value where the compactifications of r n provided by such algebras plays an important role these parametrized measures are useful in connection with the existence of correctors in homogenization problems we apply this framework to the homogenization of a porous medium type equation in r n with a stationary continuous process as a stiff oscillatory external source this application seems to be new even in the classical context of periodic homogenization

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

nonsynchronized state estimation of multichannel networked nonlinear systems with multiple packet dropouts via t s fuzzy affine dynamic models this paper investigates the problem of robust h state estimation for a class of multichannel networked nonlinear systems with multiple packet dropouts the nonlinear plant is represented by takagi sugeno t s fuzzy affine dynamic models with norm bounded uncertainties and stochastic variables with general probability distributions are adopted to characterize the data missing phenomenon in output channels the objective is to design an admissible state estimator guaranteeing the stochastic stability of the resulting estimation error system with a prescribed h disturbance attenuation level it is assumed that the plant premise variables which are often the state variables or their functions are not measurable so that the estimator implementation with state space partition may not be synchronized with the state trajectories of the plant based on a piecewise quadratic lyapunov function combined with s procedure and some matrix inequality convexifying techniques two different approaches are developed to robust filtering design for the underlying t s fuzzy affine systems with unreliable communication links all the solutions to the problem are formulated in the form of linear matrix inequalities lmis finally simulation examples are provided to illustrate the effectiveness of the proposed approaches

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

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

solution to the hjb equation for lqr type problems on compact connected lie groups in this paper we provide a solution to the hjb equation associated with lqr type problems for fully actuated left invariant control systems on compact connected lie groups we obtain the corresponding algebraic differential riccati equation and in turn generalize some of the results in berkane and tayebi 2015 to a broader class of lie groups closed loop stability results are also derived

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

stabilization and performance synthesis for systems with repeated scalar nonlinearities the class of nonlinear systems described by a discrete time state equation containing a repeated scalar nonlinearity as in recurrent neural networks is considered given a plant of this form sufficient conditions are derived for 1 the parametrization of all controllers of the same form such that the closed loop is stable in the sense of a diagonally dominant lyapunov function and 2 the synthesis of a controller of the same form so that the induced norm of the closed loop is under a prescribed level several of these conditions can be written into linear matrix inequalities

a multiple lyapunov function approach to stabilization of fuzzy control systems this paper addresses stability analysis and stabilization for takagi sugeno fuzzy systems via a so called fuzzy lyapunov function which is a multiple lyapunov function the fuzzy lyapunov function is defined by fuzzily blending quadratic lyapunov functions based on the fuzzy lyapunov function approach we give stability conditions for open loop fuzzy systems and stabilization conditions for closed loop fuzzy systems to take full advantage of a fuzzy lyapunov function we propose a new parallel distributed compensation pdc scheme that feedbacks the time derivatives of premise membership functions the new pdc contains the ordinary pdc as a special case a design example illustrates the utility of the fuzzy lyapunov function approach and the new pdc stabilization method

induced l sub 2 and generalized h sub 2 filtering for systems with repeated scalar nonlinearities this paper provides complete results on the filtering problem for a class of nonlinear systems described by a discrete time state equation containing a repeated scalar nonlinearity as in recurrent neural networks both induced l sub 2 and generalized h sub 2 indexes are introduced to evaluate the filtering performance for a given stable discrete time systems with repeated scalar nonlinearities our purpose is to design a stable full order or reduced order filter with the same repeated scalar nonlinearities such that the filtering error system is asymptotically stable and has a guaranteed induced l sub 2 or generalized h sub 2 performance sufficient conditions are obtained for the existence of admissible filters since these conditions involve matrix equalities the cone complementarity linearization procedure is employed to cast the nonconvex feasibility problem into a sequential minimization problem subject to linear matrix inequalities which can be readily solved by using standard numerical software if these conditions are feasible a desired filter can be easily constructed these filtering results are further extended to discrete time systems with both state delay and repeated scalar nonlinearities the techniques used in this paper are very different from those used for previous controller synthesis problems which enable us to circumvent the difficulty of dilating a positive diagonally dominant matrix a numerical example is provided to show the applicability of the proposed theories

mean square stabilization for sampled data t s fuzzy systems with random packet dropout this paper investigates the problem of mean square stabilization for sampled data takagi sugeno t s fuzzy networked control systems with random packet dropouts the packet dropout process is modeled as a discrete time markovian chain with complete or incomplete accessible transition probability matrix based on the lyapunov function approach sufficient conditions are derived for the mean square stability the corresponding sampled data fuzzy controller design algorithm formulated in terms of linear matrix inequalities is also given based upon the stability conditions the numerical examples and simulations are provided to illustrate the usefulness of the developed theory

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

stability analysis of discrete time fuzzy dynamic systems based on piecewise lyapunov functions this paper presents a stability analysis method for discrete time takagi sugeno fuzzy dynamic systems based on a piecewise smooth lyapunov function it is shown that the stability of the fuzzy dynamic system can be established if a piecewise lyapunov function can be constructed and moreover the function can be obtained by solving a set of linear matrix inequalities that is numerically feasible with commercially available software it is also demonstrated via numerical examples that the stability result based on the piecewise quadratic lyapunov functions is less conservative than that based on the common quadratic lyapunov functions

on nonlinear h_ infty filtering for discrete time stochastic systems with missing measurements in this paper the h infin filtering problem is investigated for a general class of nonlinear discrete time stochastic systems with missing measurements the system under study is not only corrupted by state dependent white noises but also disturbed by exogenous inputs the measurement output contains randomly missing data that is modeled by a bernoulli distributed white sequence with a known conditional probability a filter of very general form is first designed such that the filtering process is stochastically stable and the filtering error satisfies h infin performance constraint for all admissible missing observations and nonzero exogenous disturbances under the zero initial condition the existence conditions of the desired filter are described in terms of a second order nonlinear inequality such an inequality can be decoupled into some auxiliary ones that can be solved independently by taking special form of the lyapunov functionals as a consequence a linear time invariant filter design problem is discussed for the benefit of practical applications and some simplified conditions are obtained finally two numerical simulation examples are given to illustrate the main results of this paper

linear programming approach to deterministic infinite horizon optimal control problems with discounting we investigate relationships between the deterministic infinite time horizon optimal control problem with discounting in which the state trajectories remain in a given compact set y and a certain infinite dimensional linear programming idlp problem we introduce the problem dual with respect to this idlp problem and obtain some duality results we construct necessary and sufficient optimality conditions for the optimal control problem under consideration and we give a characterization of the viability kernel of y we also indicate how one can use finite dimensional approximations of the idlp problem and its dual for construction of near optimal feedback controls the construction is illustrated with a numerical example

analysis of unconstrained nonlinear mpc schemes with time varying control horizon for discrete time nonlinear systems satisfying an exponential or finite time controllability assumption we present an analytical formula for a suboptimality estimate for model predictive control schemes without stabilizing terminal constraints based on our formula we perform a detailed analysis of the impact of the optimization horizon and the possibly time varying control horizon on stability and performance of the closed loop

control lyapunov functions and zubov s method for finite dimensional nonlinear control systems we study the relation between asymptotic null controllability and control lyapunov functions it is shown that control lyapunov functions clfs may be constructed on the domain of asymptotic null controllability as viscosity solutions of a first order pde that generalizes zubov s equation the solution is also given as the value function of an optimal control problem from which several regularity results may be obtained

weakly almost periodic functions and fourier stieltjes algebras of locally compact groups a noncompact locally compact group g is called an eberlein group if w g b g where w g is the algebra of continuous weakly almost periodic functions on g and b g is the uniform closure of the fourier stieltjes algebra of g we show that if g is a noncompact in group or a noncompact nilpotent group then w g b g contains a linear isometric copy of l in particular g is not an eberlein group on the other hand finite direct products of eucidean motion groups and by a result of w veech noncompact semisimple analytic groups with finite centers are eberlein groups 1 introduction let g be a locally compact group c g the space of bounded continuous complex valued functions on g with the sup norm w g the space of continuous weakly almost periodic w a p functions on g b g the fourier stieltjes algebra of g and b g its uniform closure in c g it is known that b g c w g and if g is compact then c g w g b g therefore in this paper g is assumed to be noncompact in his efforts to characterize w a p functions w f eberlein first raised the question whether for abelian g b g w g w rudin 24 made the initial contribution to this question by showing that b g c w g if g is abelian and contains a discrete subgroup which is not of bounded order and d ramirez 23 by studying discrete abelian groups with bounded orders together with the structure theorem for locally compact abelian groups was able to show that rudin s conclusion holds for all abelian groups see the monographs 4 and 11 for complete accounts of this result in this paper we will extend rudin ramirez result to include many nonabelian groups our main result is the following

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

model predictive control for want of a local control lyapunov function all is not lost we present stability results for unconstrained discrete time nonlinear systems controlled using finite horizon model predictive control mpc algorithms that do not require the terminal cost to be a local control lyapunov function the two key assumptions we make are that the value function is bounded by a k sub spl infin function of a state measure related to the distance of the state to the target set and that this measure is detectable from the stage cost we show that these assumptions are sufficient to guarantee closed loop asymptotic stability that is semiglobal and practical in the horizon length and robust to small perturbations if the assumptions hold with linear or locally linear k sub spl infin functions then the stability will be global or semiglobal for long enough horizon lengths in the global case we give an explicit formula for a sufficiently long horizon length we relate the upper bound assumption to exponential and asymptotic controllability using terminal and stage costs that are controllable to zero with respect to a state measure we can guarantee the required upper bound but we also require that the state measure be detectable from the stage cost to ensure stability while such costs and state measures may not be easy to construct in general we explore a class of systems called homogeneous systems for which it is straightforward to choose them in fact we show for homogeneous systems that the associated k sub spl infin functions are linear thereby guaranteeing global asymptotic stability we discuss two examples found elsewhere in the mpc literature including the discrete time nonholonomic integrator to demonstrate our methods for these systems we give a new result they can be globally asymptotically stabilized by a finite horizon mpc algorithm that has guaranteed robustness we also show that stable linear systems with control constraints can be globally exponentially stabilized using finite horizon mpc without requiring the terminal cost to be a global control lyapunov function

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

variance constrained filtering for uncertain stochastic systems with missing measurements in this note we consider a new filtering problem for linear uncertain discrete time stochastic systems with missing measurements the parameter uncertainties are allowed to be norm bounded and enter into the state matrix the system measurements may be unavailable i e missing data at any sample time and the probability of the occurrence of missing data is assumed to be known the purpose of this problem is to design a linear filter such that for all admissible parameter uncertainties and all possible incomplete observations the error state of the filtering process is mean square bounded and the steady state variance of the estimation error of each state is not more than the individual prescribed upper bound it is shown that the addressed filtering problem can effectively be solved in terms of the solutions of a couple of algebraic riccati like inequalities or linear matrix inequalities the explicit expression of the desired robust filters is parameterized and an illustrative numerical example is provided to demonstrate the usefulness and flexibility of the proposed design approach

a derivation theory for generalized besicovitch spaces and its application for partial differential equations we present an extension of besicovitch spaces which has its origin in the works of zhikov et al and kozlov and oleinik we show that these spaces have a similar behaviour to the l p spaces and we give a notion of derivative that allows us to treat partial differential problems in this frame to the best of our knowledge this is new even for the usual besicovitch spaces

the two scale convergence method applied to generalized besicovitch spaces the twoscale convergence method has proved to be a very useful tool for dealing with periodic homogenization problems in the present paper we develop this theory to generalized besicovitch spaces

sliding mode control for markovian jump repeated scalar nonlinear systems with packet dropouts the uncertain occurrence probabilities case abstract this paper studies the sliding mode based control problem for a class of delayed markovian jump repeated scalar nonlinear systems rsnss subject to packet dropouts pds and randomly occurring uncertainties rous here the phenomenon of the markovian pds is modeled by utilizing a random variable obeying markov process by using the bernoulli distributed random variables the rous under uncertain occurrence probabilities uops are characterized from the mathematical perspective in addition the time delay considered is bounded time varying with known upper and lower bounds the attention is on designing a sliding mode based control method for markovian jump rsnss in the simultaneous presence of markovian pds rous and time varying delays specifically the robustly asymptotically mean square stability is ensured for corresponding sliding mode dynamics by proposing new sufficient criterion moreover the reachability in discrete setting is analyzed i e the state trajectories of the system from any initial condition are globally driven onto a small region nearby the pre designed sliding surface in mean square sense by synthesizing a robust sliding mode control smc law finally the effectiveness of developed control method is verified by some simulations

stability analysis of discrete time infinite horizon optimal control with discounted cost we analyze the stability of general nonlinear discrete time systems controlled by an optimal sequence of inputs that minimizes an infinite horizon discounted cost first assumptions related to the controllability of the system and its detectability with respect to the stage cost are made uniform semiglobal and practical stability of the closed loop system is then established where the adjustable parameter is the discount factor stronger stability properties are thereupon guaranteed by gradually strengthening the assumptions next we show that the lyapunov function used to prove stability is continuous under additional conditions implying that stability has a certain amount of nominal robustness the presented approach is flexible and we show that robust stability can still be guaranteed when the sequence of inputs applied to the system is no longer optimal but near optimal we also analyze stability for cost functions in which the importance of the stage cost increases with time opposite to discounting finally we exploit stability to derive new relationships between the optimal value functions of the discounted and undiscounted problems when the latter is well defined

unconstrained model predictive control and suboptimality estimates for nonlinear continuous time systems this paper presents a continuous time version of recent results on unconstrained nonlinear model predictive control mpc schemes based on a controllability assumption and a corresponding infinite dimensional optimization problem performance estimates and stability conditions are derived in terms of the prediction horizon and the sampling time of the mpc controller moreover improved estimates for small sampling times are discussed and a comparison to the application of the discrete time results in a sampled data context is provided

homogenization of a stochastic nonlinear reaction diffusion equation with a large reaction term the almost periodic framework abstract homogenization of a stochastic nonlinear reaction diffusion equation with a large nonlinear term is considered under a general besicovitch almost periodicity assumption on the coefficients of the equation we prove that the sequence of solutions of the said problem converges in probability towards the solution of a rather different type of equation namely the stochastic nonlinear convection diffusion equation which we explicitly derive in terms of appropriate functionals we study some particular cases such as the periodic framework and many others this is achieved under a suitable generalized concept of convergence for stochastic processes