delay dependent h filtering for singular markovian jump systems with general uncomplete transition probabilities this paper is devoted to the investigation of the delay dependent h filtering problem for a kind of singular markovian jump time delay systems with general unknown transition probabilities in this model the transition rates of the jumping process are assumed to be partly available that is some elements have been exactly known some ones have been merely known with lower and upper bounds others may have no information to use using the lyapunov functional theory a stochastically stable filter is designed to guarantee both the mean square exponential admissibility and a prescribed level of h performance for the singular markovian jump time delay systems with general unknown transition probabilities a sufficient condition is derived for the existence of such a desired filter in terms of linear matrix inequalities lmis a numerical example is provided to demonstrate the effectiveness of the proposed theory

robust h sup spl infin filtering for uncertain markovian jump systems with mode dependent time delays this paper considers the problem of robust h sup spl infin filtering for uncertain markovian jump linear systems with time delays which are time varying and depend on the system mode the parameter uncertainties are time varying norm bounded the aim of this problem is to design a markovian jump linear filter that ensures robust exponential mean square stability of the filtering error system and a prescribed l sub 2 induced gain from the noise signals to the estimation error for all admissible uncertainties a sufficient condition for the solvability of this problem is obtained the desired filter can be constructed by solving a set of linear matrix inequalities an illustrative numerical example is provided to demonstrate the effectiveness of the proposed approach

network based h filtering using a logic jumping like trigger this paper is concerned with the network based h filtering for a stochastic system where data transmission from the stochastic system to a filter is completed via a communication network network induced delays packet dropouts and packet disorders are unavoidable due to the use of the network first a logic zero order hold zoh is designed to discard the disordered packets actively the network induced delays and packet dropouts are modeled as an interval time varying delay by decomposing the delay interval into n subintervals uniformly the filter to be designed is modeled as a markov jumping filter with n modes governed by a markov chain in order to work out the transition rate from one mode to another a logic jumping like trigger is embedded into the logic zoh to simulate the switching of the markov process second based on the markov jumping filter model together with a new integral inequality in the stochastic setting a novel bounded real lemma is presented to ensure that the resultant filtering error system is mean exponentially stable with a prescribed h performance then a sufficient condition on the existence of desired markov jumping filters is provided in terms of a set of linear matrix inequalities finally an air vehicle system is employed to show effectiveness of the proposed design method

robust h observer design of linear time delay systems with parametric uncertainty abstract this paper deals with the problem of h observer design for a class of uncertain linear systems with delayed state and parameter uncertainties this problem aims at designing the linear state observers such that for all admissible parameter uncertainties the observation process remains robustly stable and the transfer function from exogenous disturbances to error state outputs meets the prespecified h norm upper bound constraint independently of the time delay the time delay is assumed to be unknown and the parameter uncertainties are allowed to be norm bounded and appear in all the matrices of the state space model an effective matrix inequality methodology is developed to solve the proposed problem we derive the conditions for the existence of the desired robust h observers and then characterize the analytical expression of these observers in terms of some free parameters a numerical example demonstrates the validity and applicability of the present approach

passivity based sliding mode control of uncertain singular markovian jump systems with time varying delay and nonlinear perturbations in this paper a sliding mode control smc with passivity of uncertain singular markovian jump systems smjs with time varying delay and nonlinear perturbations is investigated firstly a new integral type switching surface is designed secondly by introducing free matrix method and lyapunov functionals a delay dependent sufficient condition in terms of strict linear matrix inequalities lmi is derived for the resulting sliding mode dynamics such that the closed loop system is stochastically admissible and robustly passive for all admissible uncertainties thirdly a smc law is synthesized to drive the system trajectories onto the predefined switching surface in a finite time finally numerical examples are provided to demonstrate the effectiveness of the proposed method

h fixed lag smoothing for linear discrete time varying systems with uncertain observations this paper deals with the problem of h fixed lag smoothing for linear discrete time varying systems with uncertain observations and l 2 norm bounded noise first the design of h smoother is equivalent to the problem that a certain indefinite quadratic form with respect to a new state space constraints has a minimum and the smoother is such that the minimum is positive then by introducing a krein space stochastic system and applying re organized innovation analysis approach the minimum of indefinite quadratic form and its existence condition are derived finally through analyzing the existence condition of the minimum and guaranteeing the positivity of the minimum a sufficient and necessary condition for the existence of an h smoother is proposed and the smoother is obtained in terms of two standard riccati difference equations a numerical example is given to show the effectiveness of the proposed method

controller design for markov jumping systems subject to actuator saturation in this paper the stochastic stabilization problem for a class of markov jumping linear systems mjls subject to actuator saturation is considered the concept of domain of attraction in mean square sense is used to analyze the closed loop stability when the jumping mode is available a mode dependent state feedback controller is developed otherwise we give a less conservative approach to design the mode independent state feedback controller both design procedures can be converted into a set of linear matrix inequalities lmis finally a numerical example is provided to show the effectiveness of the techniques

global solvability on compact nilmanifolds of three or more steps we apply the methods of representation theory of nilpotent lie groups to study the convergence of fourier series of smooth global solutions to first order invariant partial differential equations df g in coo of a compact nilmanifold of three or more steps we investigate which algebraically welldefined conditions on d in the complexified lie algebra imply that smooth infinite dimensional irreducible solutions when they exist satisfy estimates strong enough to guarantee uniform convergence of the irreducible or primary fourier series to a smooth global solution this extends and improves the results of an earlier two step paper 0 introduction and preliminaries let n be a nilpotent lie group f n a compact nilmanifold and d a differential operator left invariant on n and viewed on f n if g e cco f n and if g is the orthogonal component of g in some irreducible subspace corresponding to the irreducible unitary representation ir then g7 e c f n too 2 modulo unitary equivalence we may think of g as being a c vector in any concrete realization or model of ir we will determine algebraically well defined conditions on first order and suitable higher order d under which the global solvability of df g in c f n is equivalent to the solvability of 7r d f g in the coo vectors for each ir in the spectrum of f n in one sense we will be presenting algebraic conditions on d for the reduction of a global geometrical problem on f n to a collection of purely group representation theoretic problems none of which needs to be regarded as living on the manifold f n operators d admitting such a reduction are called globally regular definition 0 1 in effect we will prove global regularity for suitable operators by showing that if the smooth solutions f of 7r d f g exist for each ir then they can be summed uniformly to a smooth global solution of df g globally regular operators are usually neither locally solvable nor onto c o f n 12 in order to make the necessary estimates on f7r we construct a suitable schrodinger model of ir which for convenience is not in the hilbert space l2 f n in this paper we extend to nilmanifolds of three or more steps and correct some of the results for two step nilmanifolds presented in 7 in order to describe the main results it will be helpful to review the classical situation on a torus t2 of two dimensions the situation being similar for tn with n 2 let d acl cx 3c cy and suppose for simplicity that a and 3 are real received by the editors july 24 1984 and in revised form april 10 1986 1980 mathematics subject classification 1985 revision primary 22e27 22e30 secondary 22e25 this research was supported in part by the national science foundation 1987 american mathematical society 0002 9947 87 1 00 25 per page

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

delay dependent exponential stability for a class of neural networks with time delays this paper is concerned with the exponential stability of a class of delayed neural networks described by nonlinear delay differential equations of the neutral type in terms of a linear matrix inequality lmi a sufficient condition guaranteeing the existence uniqueness and global exponential stability of an equilibrium point of such a kind of delayed neural networks is proposed this condition is dependent on the size of the time delay which is usually less conservative than delay independent ones the proposed lmi condition can be checked easily by recently developed algorithms solving lmis examples are provided to demonstrate the effectiveness and applicability of the proposed criteria

mode independent cal h _ infty filters for markovian jump linear systems this note addresses the problem of hinfin filtering for continuous time linear systems with markovian jumping parameters the main contribution of the note is to provide a method for designing an asymptotically stable linear time invariant hinfin filter for systems where the jumping parameter is not accessible the cases where the transition rate matrix of the markov process is either exactly known or unknown but belongs to a given polytope are treated the robust hinfin filtering problem for systems with polytopic uncertain matrices is also considered and a filter design method based on a lyapunov function that depends on the uncertain parameters is developed the proposed filter designs are given in terms of linear matrix inequalities

a fuzzy logic based approach to qualitative modeling this paper discusses a general approach to quali tative modeling based on fuzzy logic the method of qualitative modeling is divided into two parts fuzzy modeling and linguistic approximation it proposes to use a fuzzy clustering method fuzzy c means method to identify the structure of a fuzzy model to clarify the advantages of the proposed method it also shows some examples of modeling among them a model of a dynamical process and a model of a human operator s control action

stability and stabilization of switched linear systems with mode dependent average dwell time in this paper the stability and stabilization problems for a class of switched linear systems with mode dependent average dwell time mdadt are investigated in both continuous time and discrete time contexts the proposed switching law is more applicable in practice than the average dwell time adt switching in which each mode in the underlying system has its own adt the stability criteria for switched systems with mdadt in nonlinear setting are firstly derived by which the conditions for stability and stabilization for linear systems are also presented a numerical example is given to show the validity and potential of the developed techniques

fixed order robust h sub spl infin filter design for markovian jump systems with uncertain switching probabilities this paper discusses the fixed order robust h sub spl infin filtering problem for a class of markovian jump linear systems with uncertain switching probabilities the uncertainties under consideration are assumed to be norm bounded in the system matrices and to be elementwise bounded in the mode transition rate matrix respectively first a criterion based on linear matrix inequalities is provided for testing the h sub spl infin filtering level of a filter over all the admissible uncertainties then a sufficient condition for the existence of the fixed order robust h sub spl infin filters is established in terms of the solvability of a set of linear matrix inequalities with equality constraints to determine the filter a globally convergent algorithm involving convex optimization is suggested finally a numerical example is used to illustrate that the developed theory is more effective than the existing results

h filtering for a class of uncertain nonlinear systems abstract this paper investigates the problem of h filtering for a class of uncertain continuous time nonlinear systems with real time varying parameter uncertainty and unknown initial state we develop an infinite horizon h filtering methodology which provides both robust stability and a guaranteed h performance for the filtering error irrespective of the parameter uncertainty

stochastic stabilization of singular systems with markovian switchings this paper studies the stochastic stabilization problem for a class of singular markovian jump system the aim is to determine whether or not there is a stochastic feedback controller stabilizing a given singular markovian jump system smjs a new kind of stochastic controller only in the diffusion part is proposed such that the closed loop system has a unique solution and is almost surely exponentially admissible new sufficient condition for the existence of such a controller is given as linear matrix inequalities lmis based on this more extensions to transition probability matrix tpm with elements partially unknown and system states partially observable are developed a numerical example is used to demonstrate the effectiveness of the proposed methods

robust h sub spl infin filtering for stochastic time delay systems with missing measurements in this paper the robust hinfin filtering problem is studied for stochastic uncertain discrete time delay systems with missing measurements the missing measurements are described by a binary switching sequence satisfying a conditional probability distribution we aim to design filters such that for all possible missing observations and all admissible parameter uncertainties the filtering error system is exponentially mean square stable and the prescribed hinfin performance constraint is met in terms of certain linear matrix inequalities lmis sufficient conditions for the solvability of the addressed problem are obtained when these lmis are feasible an explicit expression of a desired robust hinfin filter is also given an optimization problem is subsequently formulated by optimizing the hinfin filtering performances finally a numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach

technical communique h state feedback control for generalized continuous discrete time delay system in this paper we consider the problem of designing h state feedback controller for the generalized time delay systems with delayed states and control inputs in continuous and discrete time cases respectively the generalized time delay system problems are solved on the basis of linear matrix inequality lmi technique considering time delays the sufficient condition for the existence of controller and h state feedback controller design methods are presented also using some changes of variables and schur complements the obtained sufficient condition can be rewritten as an lmi form in terms of transformed variables the proposed controller design method can be extended into the problem of robust h state feedback controller design method easily

a new approach of neuro fuzzy learning algorithm for tuning fuzzy rules abstract in this paper we develop a new approach of neuro fuzzy learning algorithm for tuning fuzzy rules by using training input output data based on the gradient descent method a major advantage of this approach is that fuzzy rules or membership functions can be learned without changing the form of fuzzy rule table used in usual fuzzy applications so that the case of non firing or weak firing can be well avoided which is different from the conventional neuro fuzzy learning algorithms moreover some properties of the developed approach are also discussed finally the efficiency of the developed approach is illustrated by means of identifying non linear functions

robust h_ infty filtering for switched stochastic system with missing measurements this paper considers the design of robust h infin filtering problem for switched stochastic discrete time delay system with missing measurements via switched lyapunov function approach attention is focused on the design of an exponentially stable filter guaranteeing a prescribed noise attenuation level in the h infin sense and missing measurements probability by using switched lyapunov functionals some sufficient conditions in terms of linear matrix inequalities lmis are obtained finally a numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach

a genetic based neuro fuzzy approach for modeling and control of dynamical systems linguistic modeling of complex irregular systems constitutes the heart of many control and decision making systems and fuzzy logic represents one of the most effective algorithms to build such linguistic models in this paper a linguistic qualitative modeling approach is proposed the approach combines the merits of the fuzzy logic theory neural networks and genetic algorithms gas the proposed model is presented in a fuzzy neural network fnn form which can handle both quantitative numerical and qualitative linguistic knowledge the learning algorithm of a fnn is composed of three phases the first phase is used to find the initial membership functions of the fuzzy model in the second phase a new algorithm is developed and used to extract the linguistic fuzzy rules in the third phase a multiresolutional dynamic genetic algorithm mrd ga is proposed and used for optimized tuning of membership functions of the proposed model two well known benchmarks are used to evaluate the performance of the proposed modeling approach and compare it with other modeling approaches

stochastic stability properties of jump linear systems jump linear systems are defined as a family of linear systems with randomly jumping parameters usually governed by a markov jump process and are used to model systems subject to failures or changes in structure the authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties it is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability and a testable necessary and sufficient condition for second moment stability is derived the lyapunov exponent method for the study of almost sure sample stability is discussed and a theorem which characterizes the lyapunov exponents of jump linear systems is presented finally for one dimensional jump linear system it is proved that the region for delta moment stability is monotonically converging to the region for almost sure stability at delta down arrow 0 sup

the extended kalman filter as an exponential observer for nonlinear systems we analyze the behavior of the extended kalman filter as a state estimator for nonlinear deterministic systems using the direct method of lyapunov we prove that under certain conditions the extended kalman filter is an exponential observer i e the dynamics of the estimation error is exponentially stable furthermore we discuss a generalization of the kalman filter with exponential data weighting to nonlinear systems

adaptive fuzzy control for synchronization of nonlinear teleoperators with stochastic time varying communication delays in this paper adaptive fuzzy control is investigated for nonlinear teleoperators with time delays which ensures synchronization of positions and velocities of the master and slave manipulators and does not rely on the use of the scattering transformation compared with the previous passivity framework the communication delays are assumed to be stochastic time varying by feedback linearization the nonlinear dynamics of the teleoperation system is transformed into two subsystems local master slave position control with unmodeled dynamics and delayed motion synchronization then based on linear matrix inequalities lmi and markov jump linear systems adaptive fuzzy control strategies are developed for the nonlinear teleoperators with modeling uncertainties and external disturbances by using the approximation property of the fuzzy logic systems it is proven that the master slave teleoperation system is stochastically stable in mean square under specific lmi conditions and all the signals of the resulting closed loop system are uniformly bounded finally the extensive simulations are performed to show the effectiveness of the proposed method

robust h spl infin filter design for uncertain linear systems with multiple time varying state delays the problem of robust h spl infin filtering for continuous time uncertain linear systems with multiple time varying delays in the state variables is investigated the uncertain parameters are supposed to belong to a given convex bounded polyhedral domain the aim is to design a stable linear filter assuring asymptotic stability and a prescribed h spl infin performance level for the filtering error system irrespective of the uncertainties and the time delays sufficient conditions for the existence of such a filter are established in terms of linear matrix inequalities which can be efficiently solved by means of powerful convex programming tools with global convergence assured an example illustrates the proposed methodology

positive operator based iterative algorithms for solving lyapunov equations for ito stochastic systems with markovian jumps this paper studies the iterative solutions of lyapunov matrix equations associated with ito stochastic systems having markovian jump parameters for the discrete time case when the associated stochastic system is mean square stable two iterative algorithms with one in direct form and the other one in implicit form are established the convergence of the implicit iteration is proved by the properties of some positive operators associated with the stochastic system for the continuous time case a transformation is first performed so that it is transformed into an equivalent discrete time lyapunov equation then the iterative solution can be obtained by applying the iterative algorithm developed for discrete time lyapunov equation similar to the discrete time case an implicit iteration is also proposed for the continuous case for both discrete time and continuous time lyapunov equations the convergence rates of the established algorithms are analyzed and compared numerical examples are worked out to validate the effectiveness of the proposed algorithms

network based h_ infty filtering for discrete time systems this correspondence is concerned with network based h filtering for discrete time systems the output signals of the system under consideration are transmitted to the filter through a constraint communication network which usually leads to network induced delays and packet dropouts by introducing a logic data packet processor to choose the newest data signal from the network to actuate the filter network induced delays and packet dropouts are modeled as a markov chain taking values in a finite set as a result the filter to be designed is modeled as a markov jumping linear filter by introducing some slack matrix variables in terms of prob ability identity a less conservative bounded real lemma brl is derived to ensure that the filtering error system is stochastically stable with a pre scribed h level based on this brl suitable h filters are designed by employing a cone complementary approach a practical example on the leslie model about some certain pest s structured population dynamics is given to show the effectiveness of the proposed approach

a near optimal multiuser detector for ds cdma systems using semidefinite programming relaxation a multiuser detector for direct sequence code division multiple access systems based on semidefinite programming sdp is proposed it is shown that maximum likelihood ml detection can be carried out by relaxing the associated integer programming problem to a dual sdp problem which leads to a detector of polynomial complexity computer simulations that demonstrate that the proposed detector offers near optimal performance with considerably reduced computational complexity compared with that of existing primal sdp relaxation based detectors are presented

knowledge discovery by a neuro fuzzy modeling framework in this paper a neuro fuzzy modeling framework is proposed which is devoted to discover knowledge from data and represent it in the form of fuzzy rules the core of the framework is a knowledge extraction procedure that is aimed to identify the structure and the parameters of a fuzzy rule base through a two phase learning of a neuro fuzzy network in order to obtain reliable and readable knowledge two further stages are integrated with the knowledge extraction procedure a pre processing stage performing variable selection on the available data to obtain simpler and more reliable fuzzy rules and a post processing stage that granulates outputs of the extracted fuzzy rules so as to provide a validity range of estimated outputs moreover the framework can address complex multi input multi output problems in such case two distinct modeling strategies can be followed with the opportunity of producing both a single mimo model or a collection of miso models the proposed framework is verified on a real world case study involving prediction of chemical composition of ashes produced by combustion processes carried out in thermo electric generators located in italy

h_ infty filtering of discrete time switched systems with state delays via switched lyapunov function approach in this note the problem of hinfin filtering for a class of discrete time switched systems with state delays is investigated attention is focused on the design of a stable filter guaranteeing a prescribed noise attenuation level in the hinfin sense by using switched lyapunov functionals sufficient conditions for the solvability of this problem are obtained in terms of linear matrix inequalities lmis by solving which a desired hinfin filter can be constructed a numerical example is provided to demonstrate the effectiveness of the proposed techniques

robust stability constraints for fuzzy model predictive control this paper addresses the synthesis of a predictive controller for a nonlinear process based on a fuzzy model of the takagi sugeno t s type resulting in a stable closed loop control system conditions are given that guarantee closed loop robust asymptotic stability for open loop bounded input bounded output bibo stable processes with an additive l sub 1 norm bounded model uncertainty the idea is closely related to small gain based l sub 1 control theory but due to the time varying approach the resulting robust stability constraints are less conservative therefore the fuzzy model is viewed as a linear time varying system rather than a nonlinear one the goal is to obtain constraints on the control signal and its increment that guarantee robust stability robust global asymptotic stability and offset free reference tracking are guaranteed for asymptotically constant reference trajectories and disturbances

globally hypoelliptic systems of vector fields on nilmanifolds abstract we show that a system l of real vector fields on a general compact nilmanifold n induced by the lie algebra n of n is globally hypoelliptic gh iff 1 the symbols of the vector fields of l projected onto the associated torus t n n n as functions on the integral lattice t collectively decrease at infinity not faster than a reciprocal of a polynomial and 2 the lie subalgebra of n that l generates is not annihilated by any non zero integral linear functional on any n j n j 1 j 0 1 n j 1 n n j n o n it follows that gh is equivalent to injectivity of the system l on the dual on the space of c vectors of all the non trivial representations in the spectrum of n a rockland type condition plus a number theoretic condition on l on the associated torus to avoid small divisors

robust h sub spl infin control of discrete time markovian jump linear systems with mode dependent time delays considers the class of discrete time markovian jump linear system with norm bounded uncertainties and time delay which is dependent on the system mode linear matrix inequality lmi based sufficient conditions for the stability stabilization and h sub spl infin control are developed a numerical example is worked out to show the usefulness of the theoretical results

robust h exponential filtering for uncertain stochastic time delay systems with markovian switching and nonlinearities in this paper we deal with the robust h exponential filtering problem for a class of uncertain stochastic time delay systems with markovian switching and nonlinear disturbances the system under consideration involves parameter uncertainties ito type stochastic disturbances markovian jump parameters unknown nonlinear disturbances as well as time varying delays which vary in a range and dependent on the mode of the operation the aim of this problem is to design a markovian jump exponential filter such that the filtering error system is robustly stochastically exponentially mean square stable and a prescribed h disturbance attenuation level is guaranteed novel delay range dependent sufficient conditions are proposed to guarantee the existence of the desired robust exponential filter which are derived in terms of linear matrix inequalities lmis then the explicit expression of the desired filter parameters is characterized an illustrative numerical example is provided to demonstrate the effectiveness of the proposed method

an implicit sequential algorithm for solving coupled lyapunov equations of continuous time markovian jump systems in this paper an implicit sequential algorithm is presented for solving coupled lyapunov matrix equations of continuous time markovian jump linear systems first some existing iterative algorithms which can be utilized to solve the coupled lyapunov matrix equations are reviewed and discussed next based on the existing parallel iterative algorithm an implicit sequential algorithm is proposed by using the latest updated information the proposed algorithm fills the current gap of implicit algorithms for solving continuous coupled lyapunov matrix equations it is shown that the proposed algorithm with zero initial conditions can monotonically converge to the unique positive definite solutions of the coupled lyapunov matrix equations if the associated markovian jump system is stochastically stable moreover a necessary and sufficient condition is established for the proposed algorithm to be convergent the algorithm presented in this paper has much better convergence performance than other existing iterative algorithms and requires less storage capacity finally a numerical example is given to show the effectiveness of the proposed algorithm

sliding mode control of mimo markovian jump systems this paper addresses the sliding mode control problem for uncertain mimo linear markovian jump systems firstly by using the linear matrix inequality approach sufficient conditions are proposed to guarantee the stochastically asymptotical stability of the system on the sliding surfaces secondly an equivalent control based sliding mode control is proposed such that the closed loop system can be driven onto the desired sliding surfaces in a finite time finally combining with multi step state transition probability the reaching and sliding probabilities are derived for situations where the control force may not be strong enough to ensure the fully asymptotical stability simulation results are presented to illustrate the effectiveness of the proposed design method

robust and non fragile finite time h control for uncertain markovian jump nonlinear systems this paper investigates the non fragile and robust finite time h control problem for a class of uncertain markovian jump nonlinear systems with bounded parametric uncertainties and norm bounded disturbance by employing stochastic analysis and linear matrix inequality techniques sufficient criteria of stochastic finite time boundedness and stochastic h finite time boundedness are first provided for the class of stochastic jump systems then a controller is designed such that the class of stochastic nonlinear dynamics are stochastically finite time bounded and have an h attention performance level by utilizing matrix decomposition approach furthermore the analysis and design of non fragile and robust finite time controller are provided to guarantee that the class of uncertain stochastic systems are stochastically finite time boundeded with a prescribed attention index by using non fragile control technique in addition we also deal with the analysis and design of stochastic finite time stability and stochastic finite time stabilization all criterions can be characterized in terms of linear matrix inequalities finally two examples are also given to illustrate the effectiveness of obtained results

stability analysis and control synthesis for switched systems a switched lyapunov function approach this paper addresses the problem of stability analysis and control synthesis of switched systems in the discrete time domain the approach followed in this paper looks at the existence of a switched quadratic lyapunov function to check asymptotic stability of the switched system under consideration two different linear matrix inequality based conditions allow to check the existence of such a lyapunov function the first one is classical while the second is new and uses a slack variable which makes it useful for design problems these two conditions are proved to be equivalent for stability analysis investigating the static output feedback control problem we show that the second condition is in this case less conservative the reduction of the conservatism is illustrated by a numerical evaluation

h sub spl infin filtering for fuzzy singularly perturbed systems with pole placement constraints an lmi approach this paper addresses the problem of designing an h sub spl infin filter for a class of nonlinear singularly perturbed systems described by a takagi sugeno ts fuzzy model based on a linear matrix inequality lmi approach we develop a fuzzy h sub spl infin controller that guarantees that i the l sub 2 gain from an exogenous input to a filter error is less than or equal to a prescribed value and ii the poles of each local filter are within a prespecified region in order to alleviate the ill conditioning resulting from the interaction of slow and fast dynamic modes solutions to the problem are given in terms of linear matrix inequalities which are independent of the singular perturbation spl epsiv when spl epsiv is sufficiently small the proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard but also to nonstandard singularly perturbed nonlinear systems a numerical example is provided to illustrate the design developed in this paper

trilateral teleoperation of adaptive fuzzy force motion control for nonlinear teleoperators with communication random delays in this paper an adaptive fuzzy control scheme is proposed for hybrid motion force of trilateral teleoperation systems with a dual master single slave configuration under stochastic time varying delays in communication channels different from previous works on bilateral teleoperation systems this paper addresses dual master trilateral control of a single holonomic constrained robotic manipulator where the communication delays are modeled as multiple markov chains and the motion force controls are investigated under consideration of unsymmetric stochastic time varying delays and system dynamical uncertainties using partial feedback linearization the whole trilateral teleoperation system which consists of both master and slave manipulator dynamics is transformed into three subsystems by integrating markov jump systems to handle random delays adaptive fuzzy control strategies are developed for the nonlinear teleoperators with modeling uncertainties and external disturbances by using the approximation property of the fuzzy logic systems flss it is proven that the trilateral teleoperation system is stochastically stable in mean square under specific linear matrix inequality lmi conditions and all the signals of the resulting closed loop system are uniformly bounded the proposed scheme is validated by extensive simulations

controllability stabilizability and continuous time markovian jump linear quadratic control consideration is given to the control of continuous time linear systems that possess randomly jumping parameters which can be described by finite state markov processes the relationship between appropriately defined controllability stabilizability properties and the solution of the infinite time jump linear quadratic jlq optimal control problems is also examined although the solution of the continuous time markov jlq problem with finite or infinite time horizons is known only sufficient conditions for the existence of finite cost constant stabilizing controls for the infinite time problem appear in the literature in this paper necessary and sufficient conditions are established these conditions are based on new definitions of controllability observability stabilizability and detectability that are appropriate for continuous time markovian jump linear systems these definitions play the same role for the jlq problem as the deterministic properties do for the linear quadratic regulator lqr problem

delay range dependent robust h filtering for uncertain stochastic systems with mode dependent time delays and markovian jump parameters abstract this paper investigates the problem of robust h filtering for uncertain stochastic time delay systems with markovian jump parameters both the state dynamics and measurement of the system are corrupted by wiener processes the time delay varies in an interval and depends on the mode of operation a markovian jump linear filter is designed to guarantee robust exponential mean square stability and a prescribed disturbance attenuation level of the resulting filter error system a novel approach is employed in showing the robust exponential mean square stability the exponential decay rate can be directly estimated using matrices of the lyapunov krasovskii functional and its derivative a delay range dependent condition in the form of lmis is derived for the solvability of this h filtering problem and the desired filter can be constructed with solutions of the lmis an illustrative numerical example is provided to demonstrate the effectiveness of the proposed approach

iterative solutions of coupled discrete markovian jump lyapunov equations in this paper two iterative methods are given to solve coupled discrete markovian jump lyapunov equations arising from the stability analysis of discrete time markovian jump systems when such equations have unique positive definite solutions a sufficient condition for the convergence of iterates for one iterative method is derived when such equations only have unique solutions but not necessarily positive definite the above iterative method may fail and an alterative iterative method is provided by using the solutions of discrete time lyapunov equations as its intermediate steps a sufficient condition is also presented for the convergence of the iterates

stabilization of hybrid neutral stochastic differential delay equations by delay feedback control abstract this paper is concerned with the problem of exponential mean square stabilization of hybrid neutral stochastic differential delay equations with markovian switching by delay feedback control a delay feedback controller is designed in the drift part so that the controlled system is mean square exponentially stable we discussed two types of structure controls that is state feedback and output injection the stabilization criteria are derived in terms of linear matrix inequalities

event based h filtering for sampled data systems this paper is concerned with event based h filtering for sampled data systems first an event based data packet processor is introduced to release sampled measurement outputs only if an event condition is violated as a result communication resources can be saved significantly while preserving the desired h performance second the resulting filtering error system is modeled as a system with an interval time varying delay by employing the lyapunov krasovskii functional approach a new bounded real lemma brl is established such that the filtering error system is asymptotically stable with the prescribed h performance third by performing an invertible linear transformation on the filtering error system a linear matrix inequality lmi based sufficient condition which is equivalent to the condition in the brl is obtained on the feasibility of the event based h filtering problem consequently suitable h filters and the event parameters in the event condition can be co designed provided that a set of lmis are satisfied finally a mechanical system with two masses and two springs is given to show the effectiveness of the proposed method

filtering and smoothing in an h sup infinity setting the problems of filtering and smoothing are considered for linear systems in an h sup infinity setting i e the plant and measurement noises have bounded energies are in l sub 2 but are otherwise arbitrary two distinct situations for the initial condition of the system are considered the initial condition is assumed known in one case while in the other the initial condition is not known but the initial condition the plant and measurement noise are in some weighted ball of r sup n xl sub 2 finite horizon and infinite horizon cases are considered necessary and sufficient conditions are presented for the existence of estimators both filters and smoothers that achieve a prescribed performance bound and algorithms that result in performance within the bounds are developed in case of smoothers the optimal smoother is also presented the approach uses basic quadratic optimization theory in a time domain setting as a consequence of which both linear time varying and time invariant systems can be considered with equal ease in the smoothing problem for linear time varying systems one considers only the finite horizon case

brief paper stability and stabilization of continuous time singular hybrid systems in this paper the problems of stability and state feedback stabilization for a class of continuous time singular hybrid systems are investigated a new sufficient and necessary condition for a continuous time singular hybrid system to be regular impulse free and stochastically stable is proposed in terms of a set of coupled strict linear matrix inequalities lmis moreover a new sufficient and necessary condition is presented for the existence of the state feedback controller in terms of a set of coupled strict matrix inequalities finally a numerical example is given to illustrate the effectiveness of the obtained theoretical results

robust finite time h control for uncertain discrete jump systems with time delay abstract this paper addresses the robust finite time h control problem for a family of uncertain discrete time markovian jump systems with time delay initially the concepts of stochastic finite time boundedness and stochastic h finite time stabilization are given then a stochastic finite time h controller is designed such that the underlying closed loop discrete jump time delay system is stochastic finite time boundedness and satisfies a prescribed h performance level in some given finite time interval based on lyapunov approach sufficient criteria on the stochastic h finite time stabilization are established for the solvability of the problem which can be handled by a feasibility problem in the form of linear matrix inequalities with a fixed parameter finally simulation examples are presented to demonstrate the validity of the developed techniques

discrete time markovian jump linear quadratic optimal control this paper is concerned with the optimal control of discrete time linear systems that possess randomly jumping parameters described by finite state markov processes for problems having quadratic costs and perfect observations the optimal control laws and expected costs to go can be precomputed from a set of coupled riccati like matrix difference equations necessary and sufficient conditions are derived for the existence of optimal constant control laws which stabilize the controlled system as the time horizon becomes infinite with finite optimal expected cost

a delay dependent approach to robust h sub spl infin filtering for uncertain discrete time state delayed systems a delay dependent approach to robust h sub spl infin filtering is proposed for linear discrete time uncertain systems with multiple delays in the state the uncertain parameters are supposed to reside in a polytope and the attention is focused on the design of robust filters guaranteeing a prescribed h sub spl infin noise attenuation level the proposed filter design methodology incorporates some recently appeared results such as moon s new version of the upper bound for the inner product of two vectors and de oliveira s idea of parameter dependent stability which greatly reduce the overdesign introduced in the derivation process in addition to the full order filtering problem the challenging reduced order case is also addressed by using different linearization procedures both full and reduced order filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities which can be solved via efficient interior point algorithms numerical examples have been presented to illustrate the feasibility and advantages of the proposed methodologies

approximation theory of fuzzy systems spl minus siso case in this paper the approximation properties of mimo fuzzy systems generated by the product inference are discussed we first give an analysis of fuzzy basic functions fbf s and present several properties of fbf s based on these properties of fbf s we obtain several basic approximation properties of fuzzy systems 1 basic approximation property which reveals the basic approximation mechanism of fuzzy systems 2 uniform approximation bounds which give the uniform approximation bounds between the desired control or decision functions and fuzzy systems 3 uniform convergent property which shows that fuzzy systems with defined approximation accuracy can always be obtained by dividing the input space into finer fuzzy regions and 4 universal approximation property which shows that fuzzy systems are universal approximators and extends some previous results on this aspect the similarity between fuzzy systems and mathematical approximation is discussed and an idea to improve approximation accuracy is suggested based on uniform approximation bounds

robust h infinity filtering for a class of non linear systems with state delay and parameter uncertainty this paper deals with the problem of robust h infinity filtering for a class of state delayed non linear systems with normbounded parameter uncertainty appearing in all the matrices of the linear part of the system model the non linearities are assumed to satisfy the global lipschitz conditions and appear in both the state and measured output equations attention is focused on the design of a non linear filter which ensures both the robust stability and a prescribed h infinity performance of the filtering error dynamics for all admissible uncertainties a sufficient condition for the existence of such a filter is given in terms of a linear matrix inequality lmi when this lmi is feasible the expression of a desired h infinity filter is also presented a numerical example is provided to demonstrate the applicability of the proposed approach

input selection and partition validation for fuzzy modelling using neural network a simple and effective method for selecting significant input variables and determining optimal number of fuzzy rules when building a fuzzy model from data is proposed in contrast to the existing clustering based methods in this approach both input selecting and partition validating are determined on the basis of a class of sub clusters created by a self organising network instead of on the data the important input variables which independently and significantly influence the system output can be extracted by a fuzzy neural network on the other hand the optimal number of fuzzy rules can be determined separately via the fuzzy c means algorithm with a modified fuzzy entropy as the criterion of cluster validation the simulation results show that the proposed method can provide good model structures for fuzzy modelling and has high computing efficiency

p moment stability of stochastic differential equations with impulsive jump and markovian switching this paper introduces some new concepts of p moment stability for stochastic differential equations with impulsive jump and markovian switching some stability criteria of p moment stability for stochastic differential equations with impulsive jump and markovian switching are obtained by using liapunov function method an example is also discussed to illustrate the efficiency of the obtained results

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

partially mode dependent design of h filter for stochastic markovian jump systems with mode dependent time delays abstract this paper is concerned with the h filtering problem for stochastic delay systems with markovian jump parameters where both the state dynamics and measurements of systems are corrupted by wiener process in contrast with traditional mode dependent and mode independent filtering methods a new partially mode dependent filter is established via using a mode dependent lyapunov function where the system mode available to filter implementation is transmitted through an unreliable network and the stochastic property of mode available to a filter is considered sufficient conditions for the existence of h filters are obtained as linear matrix inequalities finally an example is used to show the effectiveness of the given theoretical results

brief paper h filtering for 2d markovian jump systems this paper is concerned with the problem of h filtering for 2d discrete markovian jump systems the mathematical model of 2d jump systems is established upon the well known roesser model our attention is focused on the design of a full order filter which guarantees the filtering error system to be mean square asymptotically stable and has a prescribed h disturbance attenuation performance sufficient conditions for the existence of a desired filter are established in terms of linear matrix inequalities lmis and the corresponding filter design is cast into a convex optimization problem which can be efficiently solved by using commercially available numerical software a numerical example is provided to illustrate the effectiveness of the proposed design method

brief paper robust exponential stabilization for markovian jump systems with mode dependent input delay this paper is concerned with the problem of exponential stabilization for uncertain linear systems with markovian jump parameters and mode dependent input delays sufficient stabilization conditions are developed in terms of matrix inequalities which can be solved by a proposed iterative algorithm based on the cone complementarity linearization ccl method memory controllers are also designed such that the closed loop system is exponentially mean square stable for all admissible uncertainties numerical examples are given to show that the developed method is efficient and less conservative

stabilization of singular markovian jump systems with time varying switchings this paper studies the stabilization problem for a class of singular markovian jump systems smjss with time varying transition rates by using the quantized method firstly by proposing a quantization principle the time varying transition rate matrix trm is quantized into a series of finite trms with norm bounded uncertainties then the difficulties of the time varying trm confronted in system analysis and synthesis can be overcome new criteria for stochastic admissibility analysis as well as controller synthesis are established in terms of linear matrix inequalities lmis finally the validity of the theoretical results is shown by numerical examples

robust h sub spl infin control of uncertain markovian jump systems with time delay this paper is concerned with the robust stochastic stabilizability and robust h sub spl infin disturbance attenuation for a class of uncertain linear systems with time delay and randomly jumping parameters the transition of the jumping parameters is governed by a finite state markov process sufficient conditions on the existence of a robust stochastic stabilizing and spl gamma suboptimal h sub spl infin state feedback controller are presented using the lyapunov functional approach it is shown that a robust stochastically stabilizing h sub spl infin state feedback controller can be constructed through the numerical solution of a set of coupled linear matrix inequalities