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

stability and stabilization of semi markov jump linear systems with exponentially modulated periodic distributions of sojourn time this paper is concerned with a class of discrete time semi markov jump linear systems s mjlss subject to exponentially modulated periodic emp probability density function pdf of sojourn time and the problems of stability and stabilization are addressed setting a relatively large period the considered systems are capable of approximating the general s mjlss without any requirements on sojourn time pdfs for which numerically testable stability and stabilization conditions are rather difficult to obtain necessary and sufficient criterion for mean square stability of the general s mjlss is first derived which involves an infinite number of conditions and as such not checkable however the developments lay a foundation to further establish the numerically testable conditions for the systems when the pdf of sojourn time is emp albeit the sojourn time can tend to infinity the derivations explicitly depend on the pdf of sojourn time which circumvents the difficulty in obtaining the memory transition probabilities of s mjlss the adopted lyapunov function is sojourn time dependent std by which the existence conditions of std controller are developed as well using certain techniques that can eliminate the terms of power of matrices in the stability conditions two illustrative examples including a class of population ecological systems are presented to show the validity and applicability of the developed theoretical results

optimal h model reduction via linear matrix inequalities continuous and discrete time cases necessary and sufficient conditions are derived for the existence of a solution to the continuous time and discrete time h model reduction problems these conditions are expressed in terms of linear matrix inequalities lmis and a coupling non convex rank constraint set in addition an explicit parametrization of all reduced order models that correspond to a feasible solution is provided in terms of a contractive matrix these results follow from the recent solution of the h control design problem using lmis particularly simple conditions and a simple parametrization of all solutions are obtained for the zeroth order h approximation problem and the convexity of this problem is demonstrated computational issues are discussed and an iterative procedure is proposed to solve the h model reduction problem using alternating projections although global convergence of the algorithm is not guaranteed

h filtering for nonlinear networked systems with randomly occurring distributed delays missing measurements and sensor saturation this paper is concerned with the h filtering problem for a class of networked systems subject to randomly occurring distributed state delays nonlinearities sensor saturation as well as missing measurements via unreliable communication channels the output measurements are affected by sensor saturation which is described by sector nonlinearities the missing measurement is modeled as a linear random variable satisfying the bernoulli distribution and the nonlinearities with the form of global lipschitz cover the well known nonlinear functions the purpose of the addressed problem is to design a full order filter such that in the simultaneous presence of distributed delays randomly occurring nonlinearities sensor saturation and missing measurements the filtering dynamic system is guaranteed to be exponentially mean square stable and the h filtering performance index is achieved a sufficient condition for the solution of the addressed problem is derived and the explicit expression of the desired filter gains is described in terms of the solution to linear matrix inequality lmi finally a numerical example is provided to show the effectiveness of the designed method

stochastic stability of jump linear systems in this note some testable conditions for mean square i e second moment stability for discrete time jump linear systems with time homogenous and time inhomogenous finite state markov chain form processes are presented

on homogeneous convex cones the caratheodory number and the duality mapping using three simple examples we answer three questions related to homogeneous convex cones the caratha odory number of convex cones and self concordant barriers for convex cones first we show that if the convex cone is not homogeneous then the duality mapping does not have to be an involution next we show that there are very elementary convex cones that are not homogeneous but have invariant caratha odory number in the interior third we show that the invariance of the caratha odory number in the interior of the convex cone does not suffice to make the cone homogeneous even if the cone is self dual finally we characterize the caratha odory number of epigraphs of matrix norms

stability of discrete time delayed impulsive linear systems with application to multi tracking this paper studies the stability issue for discrete time delayed impulsive systems ddis the ddis model is formulated from a discrete time delayed system with impulses by using the matrix spectrum theory the estimates of solution with growth exponent are derived for delayed difference inequalities based on these results two types of criteria on exponential stability with an estimated convergence rate have been established for ddis the first type investigates the effect of destabilising impulses while the second is for the case in which the impulses stabilise the unstable discrete time delayed systems as the application the stability results are used to solve the multi tracking issue for discrete time dynamical networks by mixed impulsive networked control minc in which the impulsive control signals are transmitted via a communication network the effect of data dropout of impulsive control signals is also investigated and the maximal allowable dropout rate is estimated for the designed minc

lq control of discrete time jump systems with markov chain in a general borel space in this technical note it is studied the lq optimal control problem for discrete time markov jump linear systems considering the case in which the markov chain takes values in a general borel space cal m it is shown that the solution of the lq optimal control problem is obtained in terms of the positive semi definite solution s ell ell in cal m of cal m coupled algebraic riccati equations by cal m coupled we mean that the algebraic riccati equations are coupled via an integral over a transition probability kernel cal g cdot vert cdot having a density g cdot vert cdot with respect to a sigma finite measure mu on cal m it is obtained sufficient conditions based on the concept of stochastic stabilizability and stochastic detectability for the existence and uniqueness of this positive semi definite solution these results generalize previous ones in the literature which considered only the case of the markov chain taking values in a finite or infinite countable space

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

brief stochastic optimal control and analysis of stability of networked control systems with long delay in this paper stochastic optimal controllers of networked control systems whose network induced delay is longer than a sampling period are designed for the two cases of the system with either full state information or partial state information the controllers are shown to render corresponding networked control systems exponentially mean square stable the optimal estimator of the system state is presented when the system has partial state information and network induced delay is longer than a sampling period the separation theorem is proved to still hold in such networked control systems

a priori estimates of smoothness of solutions to difference bellman equations with linear and quasi linear operators a priori estimates for finite difference approximations for the first and second order derivatives are obtained for solutions of parabolic equations described in the title

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

output feedback stabilization of networked control systems with random delays modeled by markov chains this note investigates the output feedback stabilization of networked control systems ncss the sensor to controller s c and controller to actuator c a random network induced delays are modeled as markov chains the focus is on the design of a two mode dependent controller that depends on not only the current s c delay but also the most recent available c a delay at the controller node the resulting closed loop system is transformed to a special discrete time jump linear system then the sufficient and necessary conditions for the stochastic stability are established further the output feedback controller is designed via the iterative linear matrix inequality lmi approach simulation examples illustrate the effectiveness of the proposed method

control of linear switched systems with receding horizon modal information we provide an exact solution to two performance problems one of disturbance attenuation and one of windowed variance minimization subject to exponential stability considered are switched systems whose parameters come from a finite set and switch according to a language such as that specified by an automaton the controllers are path dependent having finite memory of past plant parameters and finite foreknowledge of future parameters exact convex synthesis conditions for each performance problem are expressed in terms of nested linear matrix inequalities the resulting semidefinite programming problem may be solved offline to arrive at a suitable controller a notion of path by path performance is introduced for each performance problem leading to improved system performance non regular switching languages are considered and the results are extended to these languages two simple physically motivated examples are given to demonstrate the application of these results

characterization of the barrier parameter of homogeneous convex cones we characterize the smallest best barrier parameter of self concordant barriers for homogeneous convex cones in particular we prove that this parameter is the same as the rank of the cone which is the number of steps in a recursive construction of the cone siegel domain construction we also provide lower bounds on the barrier parameter in terms of the caratheodory number of the cone the bounds are tight for homogeneous self dual cones 1998 the mathematical programming society inc published by elsevier science b v

a bound on the caratheodory number abstract the caratheodory number k of a pointed closed convex cone k is the minimum among all the for which every element of k can be written as a nonnegative linear combination of at most elements belonging to extreme rays caratheodory s theorem gives the bound k dim k in this work we observe that this bound can be sharpened to k l k 1 where l k is the length of the longest chain of nonempty faces contained in k thus tying the caratheodory number with a key quantity that appears in the analysis of facial reduction algorithms we show that this bound is tight for several families of cones which include symmetric cones and the so called smooth cones we also give a simple example showing that this bound can also fail to be sharp in addition we furnish a new proof of a result by guler and tuncel which states that the caratheodory number of a symmetric cone is equal to its rank finally we connect our discussion to the notion of cp rank for completely positive matrices

stochastic optimal control of unknown linear networked control system in the presence of random delays and packet losses in this paper the stochastic optimal control of linear networked control system ncs with uncertain system dynamics and in the presence of network imperfections such as random delays and packet losses is derived the proposed stochastic optimal control method uses an adaptive estimator ae and ideas from q learning to solve the infinite horizon optimal regulation of unknown ncs with time varying system matrices next a stochastic suboptimal control scheme which uses ae and q learning is introduced for the regulation of unknown linear time invariant ncs that is derived using certainty equivalence property update laws for online tuning the unknown parameters of the ae to obtain the q function are derived lyapunov theory is used to show that all signals are asymptotically stable as and that the estimated control signals converge to optimal or suboptimal control inputs simulation results are included to show the effectiveness of the proposed schemes the result is an optimal control scheme that operates forward in time manner for unknown linear systems in contrast with standard riccati equation based schemes which function backward in time

error bounds for monotone approximation schemes for parabolic hamilton jacobi bellman equations we obtain nonsymmetric upper and lower bounds on the rate of convergence of general monotone approximation numerical schemes for parabolic hamilton jacobi bellman equations by introducing a new notion of consistency our results are robust and general they improve and extend earlier results by krylov barles and jakobsen we apply our general results to various schemes including crank nicholson type finite difference schemes splitting methods and the classical approximation by piecewise constant controls in the first two cases our results are new and in the last two cases the results are obtained by a new method which we develop here

the p cones in dimension n 3 are not homogeneous when p 2 abstract using the t algebra machinery we show that up to linear isomorphism the only strictly convex homogeneous cones in r n n 3 are the 2 cones also known as lorentz cones or second order cones in particular this shows that the p cones are not homogeneous when p 2 1 p and n 3 thus answering a problem proposed by gowda and trott

quadratic control with partial information for discrete time jump systems with the markov chain in a general borel space this paper deals with the finite horizon quadratic optimal control problem of discrete time markov jump linear systems mjls considering the case in which the markov chain takes values in a general borel space s it is assumed that the controller has access to an output variable as well as the jump parameter the goal is to design a dynamic markov jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time it is shown that an optimal controller can be obtained from two s coupled difference riccati equations one associated to a filtering problem and the other one associated to a control problem in which the state variable is fully available by s coupled it is meant that the difference riccati equations are coupled via an integral over s this result which can be seen as a separation principle for discrete time mjls generalizes previous ones that were restricted to the markov chain taking values in a finite set

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

geometry of homogeneous convex cones duality mapping and optimal self concordant barriers we study homogeneous convex cones we first characterize the extreme rays of such cones in the context of their primal construction due to vinberg and also in the context of their dual construction due to rothaus then using these results we prove that every homogeneous cone is facially exposed we provide an alternative proof of a result of guler and tunc el that the siegel rank of a symmetric cone is equal to its caratheodory number our proof does not use the jordan von neumann wigner characterization of the symmetric cones but it easily follows from the primal construction of the homogeneous cones and our results on the geometry of homogeneous cones in primal and dual forms we study optimal self concordant barriers in this context we briefly discuss the duality mapping in the context of automorphisms of convex cones and prove using numerical integration that the duality mapping is not an involution on certain self dual cones

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

delay dependent sampled data control based on delay estimates in this paper the sampled data stabilization of linear time invariant systems with feedback delay is considered we assume that the delay is time varying and that its value is approximatively known we investigate how to use the available information about the evolution of delays for adapting the control law in real time numerical methods for the design of a delay dependent controller are presented this allows for providing a control for some cases in which the stabilization cannot be ensured using a controller with a fixed structure

modeling and control of ito stochastic networked control systems with random packet dropouts subject to time varying sampling in this note we discuss the modeling and control of a class of ito stochastic networked control systems ncss with packet dropouts that are subject to time varying sampling the system under consideration is first modeled as a continuous time system with input delay that is subject to double randomness via the input delay approach then by assuming the packet drop rate and recurring to the celebrated formula of total probability an equivalent model which takes full advantage of probability distribution characteristics of both packet dropouts and sampling periods is established in particular the probability distribution values of the stochastic delay taking values in two given intervals can be explicitly obtained which is of crucial importance to model and analyze the actual problem in ncss based on that robustly exponentially mean square stability of the system with an h infty performance is guaranteed an h infty controller design procedure is then proposed finally a numerical simulation example is exploited to show the effectiveness and applicability of the results derived and some less conservative results are obtained

brief paper h estimation for discrete time piecewise homogeneous markov jump linear systems this paper concerns the problem of h estimation for a class of markov jump linear systems mjls with time varying transition probabilities tps in discrete time domain the time varying character of tps is considered to be finite piecewise homogeneous and the variations in the finite set are considered to be of two types arbitrary variation and stochastic variation respectively the latter means that the variation is subject to a higher level transition probability matrix the mode dependent and variation dependent h filter is designed such that the resulting closed loop systems are stochastically stable and have a guaranteed h filtering error performance index using the idea in the recent studies of partially unknown tps for the traditional mjls with homogeneous tps a generalized framework covering the two kinds of variations is proposed a numerical example is presented to illustrate the effectiveness and potential of the developed theoretical results

h filtering of networked discrete time systems with random packet losses this paper studies the h filtering problem for networked discrete time systems with random packet losses the general multiple input multiple output mimo filtering system is considered the multiple measurements are transmitted to the remote filter via distinct communication channels and each measurement loss process is described by a two state markov chain both the mode independent and the mode dependent filters are considered and the resulting filtering error system is modelled as a discrete time markovian system with multiple modes a necessary and sufficient condition is derived for the filtering error system to be mean square exponentially stable and achieve a prescribed h noise attenuation performance the obtained condition implicitly establishes a relation between the packet loss probability and two parameters namely the exponential decay rate of the filtering error system and the h noise attenuation level a convex optimization problem is formulated to design the desired filters with minimized h noise attenuation level bound finally an illustrative example is given to show the effectiveness of the proposed results

stochastic stability in max product and max plus systems with markovian jumps we study max product and max plus systems with markovian jumps and focus on stochastic stability problems at first a lyapunov function is derived for the asymptotically stable deterministic max product systems this lyapunov function is then adjusted to derive sufficient conditions for the stochastic stability of max product systems with markovian jumps many step lyapunov functions are then used to derive necessary and sufficient conditions for stochastic stability the results for the max product systems are then applied to max plus systems with markovian jumps using an isomorphism and almost sure bounds for the asymptotic behavior of the state are obtained a numerical example illustrating the application of the stability results on a production system is also given

performance and robustness analysis of stochastic jump linear systems using wasserstein metric this paper focuses on the performance and robustness analysis of stochastic jump linear systems in the presence of stochastic jumps state variables evolve as random process with associated time varying probability density functions consequently system analysis is performed at the density level and a proper metric is necessary to quantify the system performance in this paper wasserstein metric that measures a distance between probability density functions is employed to develop new results for the performance analysis of stochastic jump linear systems both transient and steady state performance of the systems with given initial state uncertainties can be analyzed in this framework also we prove that the convergence of the wasserstein metric implies the mean square stability we present a novel split and merge algorithm for propagation of state uncertainty in such systems overall this study provides a unifying framework for the performance and robustness analysis of general stochastic jump linear systems and not necessarily markovian that is commonly assumed the usefulness and efficiency of the proposed method are verified through numerical examples

stability and stabilization of discrete time semi markov jump linear systems via semi markov kernel approach this technical note is concerned with the problems of stability and stabilization for a class of discrete time semi markov jump linear systems s mjlss the discrete time semi markov kernel smk is introduced where the probability density function of sojourn time is dependent on both current and next system mode as a consequence different types of distributions and or different parameters in a same type of distribution of sojourn time depending on the target mode towards which the system jumps can coexist in each mode of a smk the underlying s mjlss are therefore more general than those considered in existing studies a new stability concept generalizing the traditional mean square stability is proposed such that numerically testable criteria on the basis of smk are obtained numerical examples are presented to illustrate the validity and advantage of the developed theoretical results

brief paper robust fault detection for networked systems with communication delay and data missing in this paper the robust fault detection problem is investigated for a class of discrete time networked systems with unknown input and multiple state delays a novel measurement model is utilized to represent both the random measurement delays and the stochastic data missing phenomenon which typically result from the limited capacity of the communication networks the network status is assumed to vary in a markovian fashion and its transition probability matrix is uncertain but resides in a known convex set of a polytopic type the main purpose of this paper is to design a robust fault detection filter such that for all unknown inputs possible parameter uncertainties and incomplete measurements the error between the residual signal and the fault signal is made as small as possible by casting the addressed robust fault detection problem into an auxiliary robust h filtering problem of a certain markovian jumping system a sufficient condition for the existence of the desired robust fault detection filter is established in terms of linear matrix inequalities a numerical example is provided to illustrate the effectiveness and applicability of the proposed technique

brief paper stability and stabilization of markovian jump linear systems with partly unknown transition probabilities in this paper the stability and stabilization problems of a class of continuous time and discrete time markovian jump linear system mjls with partly unknown transition probabilities are investigated the system under consideration is more general which covers the systems with completely known and completely unknown transition probabilities as two special cases the latter is hereby the switched linear systems under arbitrary switching moreover in contrast with the uncertain transition probabilities studied recently the concept of partly unknown transition probabilities proposed in this paper does not require any knowledge of the unknown elements the sufficient conditions for stochastic stability and stabilization of the underlying systems are derived via lmis formulation and the relation between the stability criteria currently obtained for the usual mjls and switched linear systems under arbitrary switching are exposed by the proposed class of hybrid systems two numerical examples are given to show the validity and potential of the developed results

barrier functions in interior point methods we show that the universal barrier function of a convex cone introduced by nesterov and nemirovskii is the logarithm of the characteristic function of the cone this interpretation demonstrates the invariance of the universal barrier under the automorphism group of the underlying cone this provides a simple method for calculating the universal barrier for homogeneous cones we identify some known barriers as the universal barrier scaled by an appropriate constant we also calculate some new universal barrier functions our results connect the field of interior point methods to several branches of mathematics such as lie groups jordan algebras siegel domains differential geometry complex analysis of several variables etc

h filtering for nonuniformly sampled systems a markovian jump systems approach abstract this paper is concerned with the design of an h filter for a sampled data system where the measurement is sampled nonuniformly and randomly but the input is updated uniformly at a fast rate the process of nonuniform measurement sampling is modeled using a markov chain therefore the discrete time system together with the markov chain is a markovian jump system a mode dependent full order h filter is constructed sufficient lmi conditions are derived to ensure stochastic stability and h disturbance attenuation for the error system the case of unknown measurement sampling probabilities is also considered finally the effectiveness of the proposed approach is demonstrated through simulation results and a comparison with a general time varying h filter

on cone of nonsymmetric positive semidefinite matrices abstract in this paper we analyze and characterize the cone of nonsymmetric positive semidefinite matrices ns psd firstly we study basic properties of the geometry of the ns psd cone and show that it is a hyperbolic but not homogeneous cone secondly we prove that the ns psd cone is a maximal convex subcone of p 0 matrix cone which is not convex but the interior of the ns psd cone is not a maximal convex subcone of p matrix cone as the byproducts some new sufficient and necessary conditions for a nonsymmetric matrix to be positive semidefinite are given finally we present some properties of metric projection onto the ns psd cone

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

on energy to peak filtering for nonuniformly sampled nonlinear systems a markovian jump system approach this paper focuses on the filter design for nonuniformly sampled nonlinear systems which can be approximated by takagi sugeno t s fuzzy systems the sampling periods of the measurements are time varying and the nonuniform observations of the outputs are modeled by a homogenous markov chain a mode dependent estimator with a fast sampling frequency is proposed such that the estimation can track the signal to be estimated with the nonuniformly sampled outputs the nonlinear systems are discretized with the fast sampling period by using an augmentation technique the corresponding stochastic estimation error system is obtained by studying the stochastic stability and the energy to peak performance of the estimation error system we derive the linear matrix inequality based sufficient conditions the parameters of the mode dependent estimator can be calculated by using the proposed iterative algorithm two examples are used to demonstrate the design procedure and the efficacy of the proposed design method

linear estimation for random delay systems this paper is concerned with the linear estimation problems for discrete time systems with random delayed observations when the random delay is known online i e time stamped the random delayed system is reconstructed as an equivalent delay free one by using measurement reorganization technique and then an optimal linear filter is presented based on the kalman filtering technique however the optimal filter is time varying stochastic and does not converge to a steady state in general then an alternative suboptimal filter with deterministic gains is developed under a new criteria the estimator performance in terms of their error covariances is provided and its mean square stability is established finally a numerical example is presented to illustrate the efficiency of proposed estimators

adaptive fuzzy control for multilateral cooperative teleoperation of multiple robotic manipulators under random network induced delays in this paper an adaptive fuzzy control is investigated for multilateral teleoperation of two cooperating robotic manipulators that manipulate an object with constrained trajectory force in the presence of dynamics uncertainties and random network induced delays first the interconnected dynamics that consist of two master robots and cooperating slave robots are formulated to consider multiple stochastic delays in communication channels markov processes are used to model these random network induced delays the interconnected dynamics of the teleoperation are divided into a local master slave position force subsystem and a stochastic delayed motion synchronization subsystem then an adaptive fuzzy control strategy which is based on linear matrix inequalities lmis that combine adaptive update techniques is proposed to suppress the dynamics uncertainties the external disturbances and the multiple stochastic delays in communication channels the control approach ensures that the defined synchronization errors converge to zero the stochastic stability in mean square of the closed loop system is proved using lmis based on lyapunov krasovskii functional synthesis the proposed controls are validated using extensive simulation studies

on the rate of convergence of finite difference approximations for bellmans equations with variable coefficients the estimates presented here for parabolic bellman s equations with variable coefficients extend the ones earlier obtained for constant coefficients

brief paper robust h filtering for nonlinear stochastic systems with uncertainties and markov delays this paper investigates the h filtering problem for a class of general nonlinear stochastic systems considering model uncertainties and random time delays governed by markov chains simultaneously the general algebraic hamilton jacobi inequality hji is established first for general nonlinear stochastic systems with uncertainties and random markovian delays then a set of sufficient conditions are derived for the filtering system to achieve stochastic stability in the sense of mean square and the prescribed disturbance attenuation level moreover the developed results are specialized for a special class of nonlinear stochastic systems by presenting the sufficient conditions in terms of matrix inequalities simulation results demonstrate the effectiveness of the proposed approach

output feedback stabilization of networked control systems with a logic zero order hold this paper is concerned with output feedback stabilization of a networked control system in the discrete time domain first a logical zero order hold is introduced to select the newest data packets to drive the plant with which network induced delays and data packet dropouts can be expressed explicitly second an auxiliary vector valued function is introduced to establish a novel finite sum inequality which can provide a tighter bound than some existing ones for some finite sum term third this finite sum inequality is employed to formulate a stability criterion for the closed loop system under consideration it is proven that the stability criterion is of less conservatism than some existing ones reported in the literature fourth a cone complementary linearization based algorithm is presented to design suitable output feedback controllers finally three examples are given to show the effectiveness of the proposed method

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

stability analysis of networked control systems a sum of squares approach this paper presents a sum of squares sos approach to the stability analysis of networked control systems ncss incorporating bounded time varying delays bounded time varying transmission intervals and a shared communication medium a shared communication medium imposes that per transmission only one node which consists of several actuators or sensors can access the network and transmit its corresponding data which node obtains access is determined by a network protocol we will provide mathematical models that describe these ncss and transform them into suitable hybrid systems formulations based on these hybrid systems formulations we construct lyapunov functions using sos techniques that can be solved using lmi based computations this leads to several beneficial features i we can deal with plants and controllers which are described by nonlinear piecewise polynomial differential equations ii we can allow for non zero lower bounds on the delays and transmission intervals in contrast with various existing approaches iii we allow more flexibility in the lyapunov functions thereby obtaining less conservative estimates of the maximal allowable transmission intervals mati and maximal allowable delay mad and finally iv it provides an automated method to address stability analysis problems in ncs several numerical examples illustrate the strengths of our approach

kalman filtering for continuous time uncertain systems with markovian jumping parameters studies the problem of kalman filtering for a class of uncertain linear continuous time systems with markovian jumping parameters the system under consideration is subjected to time varying norm bounded parameter uncertainties in the state and measurement equations stochastic quadratic stability of the above system is analyzed a state estimator is designed such that the covariance of the estimation error is guaranteed to be within a certain bound for all admissible uncertainties which is in terms of solutions of two sets of coupled algebraic riccati equations

brief paper stability and stabilization of aperiodic sampled data control systems using robust linear matrix inequalities stability analysis of an aperiodic sampled data control system is considered for application to networked and embedded control the stability condition is described in a linear matrix inequality to be satisfied for all possible sampling intervals although this condition is numerically intractable a tractable sufficient condition can be constructed with the mean value theorem special attention is paid to tightness of the sufficient condition for less conservative stability analysis a region dividing technique for the reduction of conservatism and generalization to stabilization are also discussed an example demonstrates the efficacy of the approach

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

primal dual symmetry and scale invariance of interior point algorithms for convex optimization we present a definition of symmetric primal dual algorithms for convex optimization problems expressed in the conic form after describing a generalization of the space approach for such optimization problems we show that a symmetric space approach can be developed for a convex optimization problem in the conic form if and only if the underlying cone is homogeneous and self dual we provide an alternative definition of self scaled barriers and then conclude with a discussion of the scalings of the variables which keep the underlying convex cone invariant

the multidimensional truncated moment problem caratheodory numbers abstract let a be a finite dimensional subspace of c x r where x is a locally compact hausdorff space and a f 1 f m a basis of a a sequence s s j j 1 m is called a moment sequence if s j f j x d x j 1 m for some positive radon measure on x each moment sequence s has a finitely atomic representing measure the smallest possible number of atoms is called the caratheodory number c a s the largest number c a s among all moment sequences s is the caratheodory number c a in this paper the caratheodory numbers c a s and c a are studied in the case of differentiable functions methods from differential geometry are used the main emphasis is on real polynomials for a large class of spaces of polynomials in one variable the number c a is determined in the multivariate case we obtain some lower bounds and we use results on zeros of positive polynomials to derive upper bounds for the caratheodory numbers

mode independent control of singular markovian jump systems in this paper the mode independent control problem of singular markovian jump systems is firstly studied by exploiting a stochastic optimization viewpoint a new kind of mode independent h controller satisfying a minimum variance approximation is constructed whose gain is composed of some mode dependent control gains the available probability of system mode is described by the bernoulli variable and taken into account it shows that such a probability plays an important role in system analysis and associates mode independent controller with mode dependent controllers when the probability is unknown a kind of adaptive controller is proposed such that the resulting closed loop system is robust stochastically admissible with an h performance all the proposed conditions are given in terms of linear matrix inequalities two numerical examples are used to demonstrate the effectiveness of the proposed methods

exponential stability for discrete time infinite markov jump systems this technical note addresses a class of discrete time stochastic systems with infinite markov jump parameter first of all spectral criterion and lyapunov type criteria are presented for the exponential stability of considered systems further under the condition of strong detectability a barbashin krasovskii stability theorem is shown in terms of a generalized lyapunov equation with a positive semi definite term as an application of the proposed lyapunov stability criterion a sufficient condition of ell 2 input state stability is derived for the infinite markov jump systems disturbed by finite energy random disturbance

filtering s coupled algebraic riccati equations for discrete time markov jump systems abstract this paper deals with a set of s coupled algebraic riccati equations that arises in the study of filtering of discrete time linear jump systems with the markov chain in a general borel space s by s coupled it is meant that the algebraic riccati equations are coupled via an integral over s conditions for the existence and uniqueness of a positive semi definite solution to the filtering s coupled algebraic riccati equations are obtained in terms of the concepts of stochastic detectability and stochastic stabilizability this result is then applied to solve the infinite horizon minimum mean square linear markov jump filtering problem the obtained results generalize previous ones in the literature which considered only the case of the markov chain taking values in a finite state space

first derivatives estimates for finite difference schemes we give sufficient conditions under which solutions of discretized in space second order parabolic and elliptic equations perhaps degenerate admit estimates of the first derivatives in the space variables independent of the mesh size

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

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

optimal control of continuous time linear systems with a time varying random delay abstract we study a finite horizon optimal control problem for a class of linear systems with a randomly varying time delay the systems of this type may arise in embedded control applications and in certain applications in economics the delay value is treated as an unknown variable but with known statistical properties modelled by a markov process with a finite number of states the probabilistic delay averaging approach is employed to determine the optimal control in the form which is independent of the delay value

the xy centring algorithm for the dual lmi problem a new approach to fixed order control design many fixed order suboptimal control problems with stability performance and robustness specifications can be reduced to a search for a matrix x 0 satisfying a linear matrix inequality lmi while x 1 satisfies another lmi this paper defines a certain class of these problems we shall call the dual lmi problem and a computational algorithm to solve our dual lmi problem is given properties and limitations of the algorithm are discussed in comparison with the existing algorithm the min max algorithm an extension to optimal control problems is provided numerical examples for the fixed order stabilization problem and the static output feedback linear quadratic optimal control problem demonstrate the applicability of the proposed algorithm

stabilization of networked control systems with a logic zoh the technical note is concerned with the stabilization problem of networked control systems a general framework is proposed firstly where the zero order hold has the logical capability of choosing the newest control input packet the continuous time process is discretized as a system with input delays then a sufficient condition for testing the stability of the discretized system and two sufficient conditions for designing a stabilizing controller are established based upon the lyapunov theory finally numerical examples and simulations are used to illustrate the developed theory

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

controller synthesis for networked control systems this paper presents a discrete time model for networked control systems ncss that incorporates all network phenomena time varying sampling intervals packet dropouts and time varying delays that may be both smaller and larger than the sampling interval based on this model constructive lmi conditions for controller synthesis are derived such that stabilizing state feedback controllers can be designed besides the proposed controller synthesis conditions a comparison is made between the use of parameter dependent lyapunov functions and lyapunov krasovskii functions for stability analysis several examples illustrate the effectiveness of the developed theory

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

output feedback stabilization of networked control systems with packet dropouts in this paper we discuss the modeling and control of a class of networked control systems ncss with packet dropouts for the cases that there may be packet dropouts in both the backward and the forward channels in the communication network and that the network induced delays are shorter than one sampling period the closed loop ncs is modeled as a discrete time switched system with four subsystems by using the asynchronous dynamical systems approach and the average dwell time method sufficient conditions for the exponential stability of the closed loop ncs are presented in terms of nonlinear matrix inequalities and the relation between the packet dropout rate and the stability of the closed loop ncs is explicitly established a procedure involving an iterative algorithm is proposed to design the observer based output feedback controllers lastly an illustrative example is given to demonstrate the effectiveness of the proposed results

brief paper optimal linear estimation for systems with multiple packet dropouts this paper is concerned with the optimal linear estimation problem for linear discrete time stochastic systems with multiple packet dropouts based on a packet dropout model the optimal linear estimators including filter predictor and smoother are developed via an innovation analysis approach the estimators are computed recursively in terms of the solution of a riccati difference equation of dimension equal to the order of the system state plus that of the measurement output the steady state estimators are also investigated a sufficient condition for the convergence of the optimal linear estimators is given simulation results show the effectiveness of the proposed optimal linear estimators

lq optimal sampled data control under stochastic delays gridding approach for stabilizability and detectability we solve a linear quadratic optimal control problem for sampled data systems with stochastic delays the delays are stochastically determined by the last few delays the proposed optimal controller

error bounds for monotone approximation schemes for hamilton jacobi bellman equations we obtain error bounds for monotone approximation schemes of hamilton jacobi bellman equations these bounds improve previous results of krylov and the authors the key step in the proof of these new estimates is the introduction of a switching system which allows the construction of approximate almost smooth supersolutions for the hamilton jacobi bellman equation

fault detection for discrete time markov jump linear systems with partially known transition probabilities in this article the fault detection fd problem for a class of discrete time markov jump linear system mjls with partially known transition probabilities is investigated the proposed systems are more general which relax the traditional assumption in markov jump systems that all the transition probabilities must be completely known a residual generator is constructed and the corresponding fd is formulated as an h filtering problem by which the error between residual and fault are minimised in the h sense the linear matrix inequality based sufficient conditions for the existence of fd filter are derived a numerical example on a multiplier accelerator model economic system is given to illustrate the potential of the developed theoretical results

lq nash games with random entrance an infinite horizon major player and minor players of finite horizons we study dynamic games with randomly entering players staying in the game for different lengths of time particularly a class of discrete time linear quadratic lq games involving a major player who has an infinite time horizon and a random number of minor players is considered the number of the new minor players entering at some instant of time is random and it is described by a markov chain the problem of the characterization of a nash equilibrium consisting of linear feedback strategies is reformulated as a set of coupled finite and infinite horizon lq optimal control problems for markov jump linear systems mjls sufficient conditions characterizing nash equilibrium are then derived the problem of games involving a large number of minor players is then addressed using a mean field mf approach and asymptotic varepsilon nash equilibrium results are derived sufficient conditions for the existence of a mf nash equilibrium are finally stated

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

invariance and efficiency of convex representations we consider two notions for the representations of convex cones g representation and lifted g representation the former represents a convex cone as a slice of another the latter allows in addition the usage of auxiliary variables in the representation we first study the basic properties of these representations we show that some basic properties of convex cones are invariant under one notion of representation but not the other in particular we prove that lifted g representation is closed under duality when the representing cone is self dual we also prove that strict complementarity of a convex optimization problem in conic form is preserved under g representations then we move to study efficiency measures for representations we evaluate the representations of homogeneous convex cones based on the smoothness of the transformations mapping the central path of the representation to the central path of the represented optimization problem

mean field games numerical methods mean field type models describing the limiting behavior as the number of players tends to infty of stochastic differential game problems have been recently introduced by j m lasry and p l lions c r math acad sci paris 343 2006 pp 619 625 c r math acad sci paris 343 2006 pp 679 684 jpn j math 2 2007 pp 229 260 numerical methods for the approximation of the stationary and evolutive versions of such models are proposed here in particular existence and uniqueness properties as well as bounds for the solutions of the discrete schemes are investigated numerical experiments are carried out

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 filtering for networked systems with multiple state delays in this paper a new robust h filter design problem is studied for a class of networked systems with multiple state delays two kinds of incomplete measurements namely measurements with random delays and measurements with stochastic missing phenomenon are simultaneously considered such incomplete measurements are induced by the limited bandwidth of communication networks and are modelled as a linear function of a certain set of indicator functions that depend on the same stochastic variable attention is focused on the analysis and design problems of a full order robust h filter such that for all admissible parameter uncertainties and all possible incomplete measurements the filtering error dynamics is exponentially mean square stable and a prescribed h attenuation level is guaranteed some recently reported methodologies such as delay dependent and parameter dependent stability analysis approaches are employed to obtain less conservative results sufficient conditions which are dependent