discrete time lq optimal control problems for infinite markov jump parameter systems optimal control problems for discrete time linear systems subject to markovian jumps in the parameters are considered for the case in which the markov chain takes values in a countably infinite set two situations are considered the noiseless case and the case in which an additive noise is appended to the model the solution for these problems relies in part on the study of a countably infinite set of coupled algebraic riccati equations icare conditions for existence and uniqueness of a positive semidefinite solution to the icare are obtained via the extended concepts of stochastic stabilizability ss and stochastic detectability sd which turn out to be equivalent to the spectral radius of certain infinite dimensional linear operators in a banach space being less than one for the long run average cost ss and sd guarantee existence and uniqueness of a stationary measure and consequently existence of an optimal stationary control policy furthermore an extension of a lyapunov equation result is derived for the countably infinite markov state space case

infinite time exact observability of volterra systems in hilbert spaces abstract we study infinite time exact observability of volterra systems in hilbert spaces sufficient conditions are established under which infinite time exact observability of a volterra system follows from that of the corresponding cauchy system without convolution term this is done by combining the composition operator method with a result about bounded below composition operators on the hardy space

composite anti disturbance control for markovian jump nonlinear systems via disturbance observer this paper is concerned with the problems of composite disturbance observer based control dobc and control for markovian jump systems with nonlinearity and multiple disturbances our aim is to design a disturbance observer to estimate the disturbance generated by an exogenous system then construct the control scheme by integrating the output of the disturbance observer with state feedback control law such that the closed loop system can be guaranteed to be stochastically stable and different types of disturbances can be attenuated and rejected by constructing a proper stochastic lyapunov krasovskii functional sufficient conditions for the existence of the desired observer and the state feedback controller are established in terms of linear matrix inequalities lmis which can be readily solved by standard numerical software finally a numerical example is provided to show the effectiveness of the proposed approaches

ℋ 2 filtering of discrete time markov jump linear systems through linear matrix inequalities this paper addresses the 2 filtering design problem of discrete time markov jump linear systems first under the assumption that the markov parameter is measured the main contribution is on the lmi characterisation of all filters such that the estimation error remains bounded by a given 2 norm level yielding the complete solution of the mode dependent filtering design problem based on this result a robust filter design to deal with convex bounded parameter uncertainty is considered second from the same lmi characterisation a design procedure for mode independent filtering design is proposed some examples are solved for illustration and comparison

energy to peak state estimation for markov jump rnns with time varying delays via nonsynchronous filter with nonstationary mode transitions in this paper the problem of energy to peak state estimation for a class of discrete time markov jump recurrent neural networks rnns with randomly occurring nonlinearities rons and time varying delays is investigated a practical phenomenon of nonsynchronous jumps between rnns modes and desired mode dependent filters is considered and a nonstationary mode transition among the filters is used to model the nonsynchronous jumps to different degrees that are also mode dependent the rons are used to model a class of sector like nonlinearities that occur in a probabilistic way according to a bernoulli sequence the time varying delays are supposed to be mode dependent and unknown but with known lower and upper bounds a priori sufficient conditions on the existence of the nonsynchronous filters are obtained such that the filtering error system is stochastically stable and achieves a prescribed energy to peak performance index further to the recent study on the class of nonsynchronous estimation problem a monotonicity is observed in obtaining filtering performance index while changing the degree of nonsynchronous jumps a numerical example is presented to verify the theoretical findings

a convex programming approach to h2 control of discrete time markovian jump linear systems in this paper we consider the h control problem for the class of discrete time 2 linear systems with parameters subject to markovian jumps using a convex programming approach we generalize the definition of the h norm from the deter2 ministic case to the markovian jump case and set a link between this norm and the observability and controllability gramians conditions for existence and derivation of a mean square stabilizing controller for a markovian jump linear system using convex analysis are established the main contribution of the paper is to provide a convex programming formulation to the h control problem so that several 2 important cases to our knowledge not analysed in previous work can be addressed regarding the transition matrix p for the markov chain two ij situations are considered the case in which it is exactly known and the case in which it is not exactly known but belongs to an appropriated convex set regarding the state variable and the jump variable the cases in which t

generalized riccati difference and differential equations abstract in this paper we investigate generalized riccati differential and difference equations obtained from standard riccati equations by adding a semidefinite perturbation term for such equations we give results on the monotonic dependence of the solutions on the coefficients and initial values as well as results on convergence of solutions

asynchronous l 2 l filtering for discrete time stochastic markov jump systems with randomly occurred sensor nonlinearities this paper is concerned with the problem of asynchronous l 2 l filtering for discrete time stochastic markov jump systems with sensor nonlinearity the sensor nonlinearity is assumed to occur randomly according to a stochastic variable satisfying the bernoulli distribution a sufficient condition is first given such that the resultant filtering error system which is a kind of nonhomogeneous markov jump system is stochastically stable with a guaranteed l 2 l performance index then the existence criterion of the desired asynchronous filter with piecewise homogeneous markov chain is proposed in terms of a set of linear matrix inequalities a numerical example is given to show the effectiveness and potential of the developed theoretical results

a stabilization algorithm for a class of uncertain linear systems abstract this paper presents an algorithm for the stabilization of a class of uncertain linear systems the uncertain systems under consideration are described by state equations which depend on time varying unknown but bounded uncertain parameters the construction of the stabilizing controller involves solving a certain algebraic riccati equation furthermore the solution to this riccati equation defines a quadratic lyapunov function which is used to establish the stability of the closed loop system this leads to a notion of quadratic stabilizability it is shown that the stabilization procedure will succeed if and only if the given uncertain linear system is quadratically stabilizable the paper also deals with a notion of overbounding for uncertain linear systems this procedure enables the stabilization algorithm to be applied to a larger class of uncertain linear systems also included in the paper are results which indicate the degree of conservativeness introduced by this overbounding process

h control for descriptor systems a matrix inequalities approach abstract this paper considers the h control problem for descriptor systems that possibly have impulsive modes and or j axis zeros first we propose matrix inequalities that give a generalized stability condition and an h norm condition for descriptor systems using these matrix inequalities we show that the solvability of a set of matrix inequalities is necessary and sufficient to the existence of a proper controller that satisfies a prescribed h norm condition as well as stabilizing the closed loop system and eliminating all impulsive modes these inequalities are equivalent to certain linear matrix inequalities to which we can get solutions whenever they exist using efficient polynomial time algorithms

robust stabilisation control for discrete time networked control systems we consider the analysis and synthesis of discrete time networked control systems ncss where the plant has additive uncertainty and the controller is updated with the sensor information at stochastic time intervals it is shown that the problem is linked to h control of linear discrete time stochastic systems and a new small gain theorem is established based on this result sufficient conditions are given for ensuring mean square stability of the ncs and the genetic algorithm is utilised to design the controller of the ncs based on a linear matrix inequality technique an illustrative example is given to demonstrate the effectiveness of our proposed method

stationary filter for linear minimum mean square error estimator of discrete time markovian jump systems we derive in this paper a stationary filter for the linear minimum mean square error estimator lmmse of discrete time markovian jump linear systems mjlss we obtain the convergence of the error covariance matrix of the lmmse to a stationary value under the assumption of mean square stability of the mjls and ergodicity of the associated markov chain it is shown that there exists a unique solution for the stationary riccati filter equation and moreover this solution is the limit of the error covariance matrix of the lmmse the advantage of this scheme is that it is very easy to implement and all calculations can be performed off line leading to a linear time invariant filter

robust h control of descriptor discrete time markovian jump systems this paper considers the stochastic stability and the robust control of descriptor discrete time systems with markovian jumping parameters in terms of linear matrix inequalities a necessary and sufficient condition is proposed which ensures a discrete time descriptor markovian jump system to be regular causal and stochastically stable a robust admissibility condition and a robust bounded real lemma are also developed based on these a sufficient condition on the existence of a state feedback controller which guarantees the robust admissibility and the performance is also given by employing the linear matrix inequality technique a robustly stabilizing state feedback controller can be constructed through the numerical solutions of linear matrix inequalities finally an example is provided to demonstrate the effectiveness of the proposed approach

a finite frequency approach to control of markov jump linear systems with incomplete transition probabilities this paper is concerned with the state feedback control of continuous markov jump linear systems with incomplete transition probabilities in finite frequency domain by developing a new technique to handle the coupling among lyapunov variable system matrix and controller parameter new sufficient conditions for the closed loop system to be stochastically stable with the required finite frequency performance are established in terms of linear matrix inequalities meanwhile the finite frequency state feedback controller is also obtained by the proposed conditions directly the validity of the proposed method is demonstrated by a numerical example

mean square stability for discrete bounded linear systems in hilbert space the asymptotic behaviour for infinite dimensional discrete linear systems driven by white noise is considered in this paper both the evolution and convergence of the state correlation operators sequence are analysed mean square stability conditions are investigated including a comparison with the deterministic stability problem the particular case of compact operators is considered in some detail

robust jump linear quadratic control a mode stabilizing solution this correspondence is concerned with optimal feedback control of a class of linear stochastic systems for a quadratic performance index the solution to this problem is known but the resulting optimal regulator does not ensure stability in every mode of operation to improve robustness a new mode stabilizing solution is defined an example illustrates the advantages of the proposed controller

asynchronous h filtering for 2d discrete markovian jump systems with sensor failure this paper investigates the problem of the asynchronous h filtering for a class of two dimensional 2d markovian jump systems with sensor failure the asynchronous phenomenon is considered to be random mismatch between system modes and candidate filters the mismatch behavior is assumed to be stochastic with a certain probability and a new markov chain is proposed to model the jumping process of the filtering error system besides a switching method is proposed to dealing with the sensor failure sufficient conditions for the existence of a desired filter such that the filtering error system is stochastically stable with a guaranteed h performance index are obtained in the form of linear matrix inequalities lmis two examples are provided to illustrate the effectiveness and advantage of the proposed method

on p p structural matrix rings abstract a ring is called a left p p ring if every principal left ideal is projective the objective here is to completely determine the left p p structural matrix rings over a von neumann regular ring

optimal quadratic control of jump linear systems with separately controlled transition probabilities abstract the optimal control of discrete time jump systems that would be linear but for randomly jumping parameters are considered these parameter jumps which are indexed by a finite state form process can be used to model systems subject to component failures or structural changes the control of such systems when the jump probabilities can be controlled by choice of a finite valued input is considered this input form control can be thought of as corresponding to a maintenance or repair policy the optimal control problem with quadratic costs whose weighting matrices depend on the jumping parameters and form control is formulated for such systems the optimal solution for finite and infinite time horizon problems is developed in addition sufficient conditions for the existence of a steady state stabilizing solution to the infinite time problem are given in terms of appropriately defined controllability and observability properties

event triggered h filtering of markov jump systems with general transition probabilities abstract this paper investigates the h filtering of markov jump systems with general transition probabilities which are known uncertain and unknown the transmission from sensor to filter is determined by a mode dependent event triggered scheme the advantage of the scheme is that no restriction is imposed on a triggering scalar employing a zero order holder the resulting filtering error system is expressed by markov jump systems with time delay with the aid of a relaxed lyapunov krasovskii functional and the finlser lemma the desired h filter gains and the related triggering parameter are solved in a uniformed framework it is shown that the proposed approach is less conservative than the existing one numerical examples are given to verify the validity of the proposed method

robust stability and stabilization of uncertain discrete time markovian jump linear systems this note deals with robust stability and control of uncertain discrete time linear systems with markovian jumping parameters systems with polytopic type parameter uncertainty in either the state space model matrices or in the transition probability matrix of the markov process are considered this note develops methods of robust stability analysis and robust stabilization in the mean square sense which are dependent on the system uncertainty the design of both mode dependent and mode independent control laws is addressed the proposed methods are given in terms of linear matrix inequalities numerical examples are provided to demonstrate the effectiveness of the derived results

mean square stochastic stability of linear time delay system with markovian jumping parameters this paper deals with the mean square stochastic stability of the class of linear time delay systems with markovian jumping parameters a delay independent sufficient condition for checking the stochastic stability of this class of systems is established a numerical example is given to show the usefulness of the proposed theoretical results

almost completely isometric embeddings between preduals of von neumann algebras abstract we will prove that if the predual of an injective von neumann algebra is embedded in the predual of another von neumann algebra almost completely isometrically then it is complemented almost completely contractively this result is the operator space analogue of dor s theorem

disturbance attenuation and h sub infinity control via measurement feedback in nonlinear systems a solution to the problem of disturbance attenuation via measurement feedback with internal stability is presented for an affine nonlinear system it is shown that the concept of disturbance attenuation in the sense of truncated l sub 2 norms can be given an interpretation in terms of the response to periodic inputs in the sense of rms amplitude even in the nonlinear setup in the case of state feedback a family of controllers is also provided the proofs of all these results are simple and provide deeper insight even in the analysis of the corresponding linear control problem

controllability observability and discrete time markovian jump linear quadratic control this paper is concerned with the controllability and observability of discrete time linear systems that possess randomly jumping parameters described by finite stale markov processes and the relationship between these properties and the solution of the infinite time jump linear quadratic jlq optimal control problem the solution of the markovian jlq problem with finite or infinite time horizons is known necessary and sufficient conditions for the existence of optimal constant control laws that lead to finite optimal expected costs as the time horizon becomes infinite are also known sufficient conditions for these steady state control laws to stabilize the controlled system are also available chizeck et al 1986 these conditions are not easy to test however various definitions of controllability and observability for stochastic systems exist in the literature these definitions are unfortunately not related to the steady state jlq control problem in a manner that is analogous to the role of deter

h and h 2 filtering for linear systems with uncertain markov transitions this paper is concerned with h and h 2 filtering for markovian jump linear systems with uncertain transition probabilities motivated by the fact that the existing results either impose severe restrictions on some key matrices or introduce some unnecessary matrix variables this paper is focused on developing a new approach to systematically relax these restrictions for filter design by applying a novel technique to eliminate the product terms between the lyapunov matrices and the filter parameters an improved condition is first obtained for analyzing the h performance of the filtering error system then sufficient conditions in terms of linear matrix inequalities are presented for designing filters with a guaranteed h filtering performance level the proposed method is further extended to h 2 filtering theoretical analyses followed by a few numerical examples show that the proposed filter design method outperforms some existing results with respect to reduction of conservatism or variables needed for computation the filter design problems for both continuous time and discrete time markovian jump linear systems are addressed in a unified framework

optimal control for unknown discrete time nonlinear markov jump systems using adaptive dynamic programming in this paper we develop and analyze an optimal control method for a class of discrete time nonlinear markov jump systems mjss with unknown system dynamics specifically an identifier is established for the unknown systems to approximate system states and an optimal control approach for nonlinear mjss is developed to solve the hamilton jacobi bellman equation based on the adaptive dynamic programming technique we also develop detailed stability analysis of the control approach including the convergence of the performance index function for nonlinear mjss and the existence of the corresponding admissible control neural network techniques are used to approximate the proposed performance index function and the control law to demonstrate the effectiveness of our approach three simulation studies one linear case one nonlinear case and one single link robot arm case are used to validate the performance of the proposed optimal control method

controllability of linear stochastic systems abstract we discuss several concepts of controllability for stochastic systems and derive sufficient and in most cases also necessary algebraic conditions for the controllability of the state and the output of white and colored noise linear systems these criteria reduce to the well known deterministic ones in the absence of noise

brief on robust stabilization of markovian jump systems with uncertain switching probabilities this brief paper is concerned with the robust stabilization problem for a class of markovian jump linear systems with uncertain switching probabilities the uncertain markovian jump system under consideration involves parameter uncertainties both in the system matrices and in the mode transition rate matrix first a new criterion for testing the robust stability of such systems is established in terms of linear matrix inequalities then a sufficient condition is proposed for the design of robust state feedback controllers a globally convergent algorithm involving convex optimization is also presented to help construct such controllers effectively finally a numerical simulation is used to illustrate the developed theory

h filtering of periodic markovian jump systems application to filtering with communication constraints in this note a bounded real lemma brl is established for discrete time periodic markov jump linear systems mjls with nonhomogeneous finite state markov chain the brl is formulated as a finite linear matrix inequality lmi feasibility problem an application to h filtering for systems subject to limited communication capacity is then presented

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

linear minimum mean square error estimation for discrete time markovian jump linear systems the linear minimum mean square error estimator lmmse for discrete time linear systems subject to abrupt changes in the parameters modeled by a markov chain spl theta k spl epsiv 1 n is considered the filter equations are derived from geometric arguments in a recursive form resulting in an on line algorithm suitable for computer implementation the author s approach is based on estimating x k 1 sub spl theta k i instead of estimating directly x k the uncertainty introduced by the markovian jumps increases the dimension of the filter to n n 1 where n is the dimension of the state variable an example where the dimension of the filter can be reduced to n is presented as well as a numerical comparison with the imm filter

on subspaces of non commutative lp spaces abstract we study some structural aspects of the subspaces of the non commutative haagerup l p spaces associated with a general non necessarily semi finite von neumann algebra if a subspace x of l p contains uniformly the spaces l p n n 1 it contains an almost isometric almost 1 complemented copy of l p if x contains uniformly the finite dimensional schatten classes s p n it contains their l p direct sum too we obtain a version of the classical kadec pelczynski dichotomy theorem for l p spaces p 2 we also give operator space versions of these results the proofs are based on previous structural results on the ultrapowers of l p together with a careful analysis of the elements of an ultrapower l p u which are disjoint from the subspace l p these techniques permit to recover a recent result of n randrianantoanina concerning a subsequence splitting lemma for the general non commutative l p spaces various notions of p equiintegrability are studied one of which is equivalent to randrianantoanina s one and some results obtained by haagerup rosenthal and sukochev for l p spaces based on finite von neumann algebras concerning subspaces of l p containing l p are extended to the general case

a new look at the robust control of discrete time markov jump linear systems abstractin this paper we make a foray in the role played by a set of four operators on the study of robust h2 and mixed h2 h control problems for discrete time markov jump linear systems these operators appear in the study of mean square stability for this class of systems by means of new linear matrix inequality lmi characterisations of controllers which include slack variables that to some extent separate the robustness and performance objectives we introduce four alternative approaches to the design of controllers which are robustly stabilising and at the same time provide a guaranteed level of h2 performance since each operator provides a different degree of conservatism the results are unified in the form of an iterative lmi technique for designing robust h2 controllers whose convergence is attained in a finite number of steps the method yields a new way of computing mixed h2 h controllers whose conservatism decreases with iteration two numerical examples illustrate the applicability

a bounded real lemma for jump systems this note presents a bounded real lemma for discrete time markovian jump linear systems mjlss we show that the linear matrix inequality in the bounded real lemma is both necessary and sufficient for this class of systems for the case of one plant mode this condition reduces to the standard necessary and sufficient condition for discrete time systems we envision this lemma being used to construct necessary and sufficient analysis and synthesis conditions for mjlss

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

reachability and controllability of switched linear discrete time systems this paper investigates the reachability and controllability issues for switched linear discrete time systems geometric characterization of controllability is presented for reversible systems the controllable sets and the reachable sets are identified in wonham s geometric approach and verifiable conditions for reachability and controllability are also presented

tensor products of operator spaces abstract in this paper we lay the foundations for a systematic study of tensor products of subspaces of c algebras to accomplish this various notions of duality are introduced and employed elementary proofs of the complete injectivity of the haagerup norm and of the extension theorem for completely bounded maps are given pisier s gamma norms are examined and found to be special cases of the haagerup norm we identify the greatest operator space cross norm and show that the spatial tensor norm is the least operator space cross norm in an appropriate sense indeed most of the elementary theory of banach space tensor norms generalizes to the category of operator spaces

h2 filtering for discrete time hidden markov jump systems abstractin this paper we consider the h2 filtering problem for a discrete time markov jump linear systemin which the markov parameter is not available in the spirit of active fault tolerant control systems it is supposed that there is a discrete time hidden markov model k k in which the observable part k represents the information coming from a detector and available to the filter while the hidden part k of the process represents the dynamics of the real system several models found in the literature are encompassed by this framework like the complete observation case the clustering information case the mode independent case and markov models in fault tolerant control we start by analysing an auxiliary filtering problem in which it is assumed that both k k are available to the filter so that necessary and sufficient conditions in terms of lmi linear matrix inequalities for the existence of the optimal filter can be obtained in the sequel we consider the realistic case

lie solvability and the identity x1 y1 x2 y2 xq yq 0 in certain matrix algebras abstract we study the interplay between the polynomial identities x 1 x 2 x 3 x q 1 0 x 1 y 1 x 2 y 2 x q y q 0 and x 1 y 1 x 2 y 2 0 in general and in certain matrix algebras which are closely related to structural matrix algebras in particular we show that if such a matrix algebra a satisfies the identity x 1 y 1 x 2 y 2 0 in particular if a satisfies the identity x 1 x 2 x 3 0 then a satisfies the identity x 1 y 1 x 2 y 2 0 and we prove a decomposition theorem for such subalgebras of upper triangular matrix algebras satisfying the engel condition and hence for such lie nilpotent subalgebras an in depth analysis of the maximum dimension of a subalgebra of the full n n matrix algebra m n f over a field f satisfying the identity x 1 y 1 x 2 y 2 x q y q 0 as obtained in 5 leads to a more detailed formula for this maximum dimension as well to a precise way of obtaining a class of examples of f subalgebras of m n f having this dimension and finally to determining exactly when a simplified version of the mentioned formula can be used

mixed h sub 2 h sub spl infin control of discrete time markovian jump linear systems in this paper we consider the mixed h sub 2 h sub spl infin control problem for the class of discrete time linear systems with parameters subject to markovian jump linear systems it is assumed that both the state variable and the jump variable are available to the controller the transition probability matrix may not be exactly known but belongs to an appropriate convex set for this controlled discrete time markovian jump linear system the problem of interest can be stated in the following way find a robust with respect to the uncertainty on the transition markov probability matrix mean square stabilizing state and jump feedback controller that minimizes an upper bound for the h sub spl infin norm under the restriction that the h sub spl infin norm is less than a prespecified value spl delta the problem of the determination of the smallest h sub spl infin norm is also addressed we present an approximate version of these problems via linear matrix inequality optimization

an lmi approach for h2 and h reduced order filtering of uncertain discrete time markov and bernoulli jump linear systems abstract this paper proposes a new approach based on parameter dependent linear matrix inequality lmi conditions associated with a scalar parameter that are sufficient to provide robust h 2 and h reduced order mode dependent partially mode dependent or mode independent filters for discrete time markov jump linear systems mjls with time invariant uncertain transition probabilities time invariant uncertainties in the state space matrices of the modes can be handled as well as main difference with respect to the existing approaches in the literature the filter matrices are obtained directly from the slack variables introduced in the conditions moreover the proposed conditions become also necessary for a particular choice of the scalar parameter when mode dependent full order filters are designed for systems without uncertainties additionally for precisely known generalized bernoulli jump systems i e the case where all the rows of the transition probability matrix are equal optimal solutions are obtained for both mode dependent and mode independent full order filters examples including one motivated by a practical application are presented to illustrate the proposed approach

minimal varieties of algebras of exponential growth abstract the exponent of a variety of algebras over a field of characteristic zero has been recently proved to be an integer through this scale we can now classify all minimal varieties of given exponent and of finite basic rank as a consequence we describe the corresponding t ideals of the free algebra and we compute the asymptotics of the related codimension sequences verifying in this setting some known conjectures we also show that the number of these minimal varieties is finite for any given exponent we finally point out some relations between the exponent of a variety and the gelfand kirillov dimension of the corresponding relatively free algebras of finite rank

robust fuzzy control for uncertain discrete time nonlinear markovian jump systems without mode observations this paper studies the robust fuzzy control problem of uncertain discrete time nonlinear markovian jump systems without mode observations the takagi and sugeno t s fuzzy model is employed to represent a discrete time nonlinear system with norm bounded parameter uncertainties and markovian jump parameters as a result an uncertain markovian jump fuzzy system mjfs is obtained a stochastic fuzzy lyapunov function flf is employed to analyze the robust stability of the uncertain mjfs which not only is dependent on the operation modes of the system but also directly includes the membership functions then based on this stochastic flf and a non parallel distributed compensation non pdc scheme a mode independent state feedback control design is developed to guarantee that the closed loop mjfs is stochastically stable for all admissible parameter uncertainties the proposed sufficient conditions for the robust stability and mode independent robust stabilization are formulated as a set of coupled linear matrix inequalities lmis which can be solved efficiently by using existing lmi optimization techniques finally it is also demonstrated via a simulation example that the proposed design method is effective

optimal control of production rate in a failure prone manufacturing system we address the problem of controlling the production rate of a failure prone manufacturing system so as to minimize the discounted inventory cost where certain cost rates are specified for both positive and negative inventories and there is a constant demand rate for the commodity produced the underlying theoretical problem is the optimal control of a continuous time system with jump markov disturbances with an infinite horizon discounted cost criterion we use two complementary approaches first proceeding informally and using a combination of stochastic coupling linear system arguments stable and unstable eigenspaces renewal theory parametric optimization etc we arrive at a conjecture for the optimal policy then we address the previously ignored mathematical difficulties associated with differential equations with discontinuous right hand sides singularity of the optimal control problem smoothness and validity of the dynamic programming equation etc to give a rigorous proof of optimality of the conjectured policy it is hoped that both approaches will find uses in other such problems also we obtain the complete solution and show that the optimal solution is simply characterized by a certain critical number which we call the optimal inventory level if the current inventory level exceeds the optimal one should not produce at all if less one should produce at the maximum rate while if exactly equal one should produce exactly enough to meet demand we also give a simple explicit formula for the optimal inventory level

colp spaces the local structure of non commutative lp spaces abstract developing the theory of col p spaces a variation of the non commutative analogue of l p spaces we provide new tools to investigate the local structure of non commutative l p spaces under mild assumptions on the underlying von neumann algebras non commutative l p spaces with grothendieck s approximation property behave locally like the space of matrices equipped with the p norm of the sequences of their singular values as applications we obtain a basis for non commutative l p spaces associated with hyperfinite von neumann algebras with separable predual von neumann algebras generated by free groups and obtain a basis for separable nuclear c algebras

on exponential almost sure stability of random jump systems this paper is concerned with a class of random jump systems represented by transition operators which includes switched linear systems with strictly stationary switching signals in infinite modes space as its special case a series of necessary and sufficient conditions are established for almost sure stability of this class of random jump systems under different scenarios the stability criteria obtained are further extended to markov jump linear systems with infinite states and hence a unified approach to describing the almost sure stability of mjlss is addressed under this context all the results in the work are developed for both the continuous and discrete time systems

uncoupled riccati iterations for the linear quadratic control problem of discrete time markov jump linear systems this paper deals with recursive methods for solving coupled riccati equations arising in the linear quadratic control for markovian jump linear systems two algorithms based on solving uncoupled riccati equations at each iteration are presented the standard method for this problem relies on finite stage approximations with receding horizon whereas the methods presented here are based on sequences of stopping times to define the terminal time of the approximating control problems the methods can be ordered in terms of rate of convergence comparisons with other methods in the current literature are also presented

h model reduction of markovian jump linear systems abstract in this paper the h model reduction problem for linear systems that possess randomly jumping parameters is studied the development includes both the continuous and discrete cases it is shown that the reduced order models exist if a set of matrix inequalities is feasible an effective iterative algorithm involving linear matrix inequalities is suggested to solve the matrix inequalities characterizing the model reduction solutions using the numerical solutions of the matrix inequalities the reduced order models can be obtained an example is given to illustrate the proposed model reduction method

mean square stabilizing solutions for discrete time coupled algebraic riccati equations in this paper we present new sufficient conditions for the existence of a mean square stabilizing solution for a set of coupled algebraic riccati equations which arises from the study of quadratic optimal control of discrete time linear systems with markov switching parameters the conditions are derived under the assumptions of mean square stabilizability and on the unobservable modes of the system and compared with existing results

cal h _ infty filtering of discrete time markov jump linear systems through linear matrix inequalities this technical note addresses the discrete time markov jump linear systems h infin filtering design problem first under the assumption that the markov parameter is measurable the main contribution is the linear matrix inequality lmi characterization of all linear filters such that the estimation error remains bounded by a given h infin norm level yielding the complete solution of the mode dependent filtering design problem based on this result a robust filter design able to deal with polytopic uncertainty is considered second from the same lmi characterization a design procedure for mode independent filtering is proposed some examples are solved for illustration and comparisons

finite horizon quadratic optimal control and a separation principle for markovian jump linear systems in this note we consider the finite horizon quadratic optimal control problem of discrete time markovian jump linear systems driven by a wide sense white noise sequence we assume that the output variable and the jump parameters are available to the controller it is desired to design a dynamic markovian jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time as in the case with no jumps we show that an optimal controller can be obtained from two coupled riccati difference equations one associated to the optimal control problem when the state variable is available and the other one associated to the optimal filtering problem this is a principle of separation for the finite horizon quadratic optimal control problem for discrete time markovian jump linear systems when there is only one mode of operation our results coincide with the traditional separation principle for the linear quadratic gaussian control of discrete time linear systems

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

monte carlo td λ methods for the optimal control of discrete time markovian jump linear systems in this paper we present an iterative technique based on monte carlo simulations for deriving the optimal control of the infinite horizon linear regulator problem of discrete time markovian jump linear systems for the case in which the transition probability matrix of the markov chain is not known we trace a parallel with the theory of td l algorithms for markovian decision processes to develop a td l like algorithm for the optimal control associated to the maximal solution of a set of coupled algebraic riccati equations care it is assumed that either there is a sample of past observations of the markov chain that can be used for the iterative algorithm or it can be generated through a computer program our proofs rely on the spectral radius of the closed loop operators associated to the mean square stability of the system being less than 1

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

stability results for discrete time linear systems with markovian jumping parameters stability results for discrete time linear systems subject to random jumps in the parameters are obtained first necessary and sufficient conditions for mean square stability mss including the case in which the system is driven by an independent wide sense stationary random sequence are derived it is shown that mss is equivalent to the spectral radius of an augmented matrix being less than one or to the existence of a solution of a certain lyapunov equation in addition it is shown that the lyapunov equation can be derived in four equivalent forms and as a by product each one gives risc to an easier to check sufficient condition these results give inter alia a unified and rather complete picture for mss of markovian jump linear systems next we derive sufficient conditions for almost sure stability of the noiseless ease finally we conclude by presenting an illustrative application to adaptive filtering where a mild condition for almost sure convergence is provided

on the balanced truncation and coprime factors reduction of markovian jump linear systems abstract the paper deals with the balanced truncation and coprime factors reduction of markovian jump linear mjl systems which can have mode varying state input and output dimensions we develop machinery for balancing mean square stable mjl system realizations using generalized gramians and strict lyapunov inequalities and provide an improved a priori upper bound on the error induced in the balanced truncation process we also generalize the coprime factors reduction method and in doing so extend the applicability of the balanced truncation technique to the class of mean square stabilizable and detectable mjl systems we provide tools to establish mean square stabilizability and detectability of the considered mjl systems in addition a notion of right coprime factorization of mjl systems and methods to construct such factorizations are given the error measure in the coprime factors reduction approach while still norm based does not directly capture the mismatch between the nominal system and the reduced order model as is the case in the balanced truncation approach where mean square stable models are considered instead the error measure is given in terms of the distance between the coprime factors realizations and thus has an interpretation in terms of robust feedback stability the paper concludes with an illustrative example which demonstrates how to apply the coprime factors model reduction approach

jump linear quadratic gaussian control in continuous time the optimal quadratic control of continuous time linear systems that possess randomly jumping parameters which can be described by finite state markov processes is addressed the systems are also subject to gaussian input and measurement noise the optimal solution for the jump linear quadratic gaussian jlqc problem is given this solution is based on a separation theorem the optimal state estimator is sample path dependent if the plant parameters are constant in each value of the underlying jumping process then the controller portion of the compensator converges to a time invariant control law however the filter portion of the optimal infinite time horizon jlqc compensator is not time invariant thus a suboptimal filter which does converge to a steady state solution under certain conditions is derived and a time invariant compensator is obtained

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

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

on stability and lq control of mjls with a markov chain with general state space we study the mean square stability and the lq control of discrete time markov jump linear systems where the markov chain has a general state space the mean square stability is characterized by the spectral radius of an operator describing the evolution of the second moment of the state vector two equivalent tests for the mean square stability are obtained based on the existence of a positive definite solution to a lyapunov equation and a uniformity result respectively an algorithm for testing the mean square stability is also developed based on the uniformity result the finite and infinite horizon lq problems are considered and their solutions are characterized by appropriate riccati integral equations an application to networked control systems ncs is finally presented and a simple example is studied via simulation

minimax estimation with intermittent observations this paper considers a problem of minimax or h state estimation with intermittent observations in this setting the disturbance in the dynamical system and the sensor noise are controlled by adversaries and the estimator receives the sensor measurements only sporadically with the availability governed by an independent and identically distributed bernoulli process we cast this problem within the framework of stochastic zero sum dynamic games we first obtain a corresponding stochastic minimax state estimator smse and an associated generalized stochastic riccati equation gsre whose evolutions depend on two parameters one that governs the random measurement arrivals and another one that quantifies the level of h disturbance attenuation we then analyze the asymptotic behavior of the sequence generated by the gsre in the expectation sense and its weak convergence specifically we obtain threshold type conditions above which the sequence generated by the gsre can be bounded both below and above in the expectation sense moreover we show that under some conditions the norm of the sequence generated by the gsre converges weakly to a unique stationary distribution finally we prove that when the disturbance attenuation parameter goes to infinity our asymptotic results are equivalent to the corresponding results from the literature on kalman filtering with intermittent observations we provide simulations to illustrate the results

a new proof of the equivalence of injectivity and hyperfiniteness for factors on a separable hilbert space abstract in 1975 a connes proved the fundamental result that injective factors on a separable hilbert space are hyperfinite in this paper a new proof of this result is presented in which the most technical parts of connes proof are avoided particularly the proof does not rely on automorphism group theory the starting point in this approach is wassermann s simple proof of injective semidiscrete together with choi and effros characterization of semidiscrete von neumann algebras as those von neumann algebras n for which the identity map on n has an approximate completely positive factorization through n n matrices

robust mode independent filtering for discrete time markov jump linear systems with multiplicative noises this paper deals with the robust mode independent linear filtering problem for discrete time markov jump linear systems with multiplicative noises it is assumed that the values of the markov chain are not available and that the parameters of the systems are subject to convex polytopic uncertainties the goal is to design a mode independent that is one that doesn t depend on the markov jump parameter dynamic linear filter such that the closed loop system is mean square stable and minimises an upper bound for the stationary expected value of the square error a linear matrix inequalities lmi formulation based on a parameter dependent lyapunov procedure is proposed to solve the problem the paper concludes with an illustrative example

controllability of stochastic linear systems in the paper necessary and sufficient conditions for various types of stochastic controllability of the linear stochastic system of the form d x ax d t bu d t c d w r x 0 x 0 are given some possible extensions are indicated as well

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

a separation principle for the continuous time lq problem with markovian jump parameters in this paper we devise a separation principle for the finite horizon quadratic optimal control problem of continuous time markovian jump linear systems driven by a wiener process and with partial observations we assume that the output variable and the jump parameters are available to the controller it is desired to design a dynamic markovian jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time as in the case with no jumps we show that an optimal controller can be obtained from two coupled riccati differential equations one associated to the optimal control problem when the state variable is available and the other one associated to the optimal filtering problem this is a separation principle for the finite horizon quadratic optimal control problem for continuous time markovian jump linear systems for the case in which the matrices are all time invariant we analyze the asymptotic behavior of the solution of the derived interconnected riccati differential equations to the solution of the associated set of coupled algebraic riccati equations as well as the mean square stabilizing property of this limiting solution when there is only one mode of operation our results coincide with the traditional ones for the lqg control of continuous time linear systems

stochastic stability of jump discrete time linear systems with markov chain in a general borel space necessary and sufficient conditions for stochastic stability ss of discrete time linear systems subject to markov jumps in the parameters are considered assuming that the markov chain takes values in a general borel space s it is shown that ss is equivalent to the spectrum radius of a bounded linear operator in a banach space being less than 1 or to the existence of a solution of a lyapunov type equation these results generalize several previous results in the literature which considered only the case of the markov chain taking values in a finite or infinite countable space

on the solution of discrete time markovian jump linear quadratic control problems abstract a necessary and sufficient condition for the existence of a positive semidefinite solution of the coupled algebraic discrete time riccati like equation occurring in markovian jump control problems is derived by verifying a simple matrix inequality it is shown that such a solution exists and can be obtained as a limit of a monotonic sequence this leads to a straightforward numerical algorithm for the computation of the solution an example is given to illustrate the proposed method

l1 gain performance analysis and positive filter design for positive discrete time markov jump linear systems a linear programming approach abstract this paper is concerned with the l 1 gain performance analysis and positive filter design for a positive discrete time markov jump linear system mjls by using a linear programming lp approach first by constructing a linear stochastic lyapunov function and introducing an equivalent deterministic positive discrete time linear system necessary and sufficient conditions in the form of lp are derived for stochastic stability and l 1 gain performance of the positive discrete time mjls then a sufficient condition on the existence of the desired positive l 1 gain filter is provided the desired positive l 1 gain filter can be designed by solving a standard lp problem the pest s structured population dynamic model is employed to illustrate the effectiveness of the proposed method

full informationh control for discrete time infinite markov jump parameter systems abstract in this paper we consider the full information discrete timeh control problem for the class of linear systems with markovian jumping parameters the state space of the markov chain is assumed to take values in a countably infinite set full information here means that the controller has access to both the state variables and jump variables a necessary and sufficient condition for the existence of a feedback controller that makes the l 2 induced norm of the system less than a prespecified bound is obtained this condition is written in terms of a set of infinite coupled algebraic riccati equations

weak detectability and the linear quadratic control problem of discrete time markov jump linear systems the paper deals with the stochastic concepts of weak detectability and weak observability for markov jump linear systems which is an special class of composite linear systems the concepts are explored here to strengthen the similarities with the corresponding concepts of deterministic detectability and observability we introduce a collection of matrices referred to as the observability matrices we show that weak observability is equivalent to full rank of each matrix in the set of observability matrices in addition we present a stochastic counterpart of the well known result on the invariance of trajectories within non observable subspaces these characterizations allow us to clarify the relationship between weak detectability and mean square detectability and to provide a testable condition for weak detectability relying on the assumption of weak detectability we develop a method for solving the linear quadratic problem that is based on iterations of uncoupled algebraic riccati equations which