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In this note, the stability analysis and stabilization problems for a class of discrete-time Markov jump linear systems with partially known transition probabilities and time-varying delays are investigated. The time-delay is considered to be time-varying and has a lower and upper bounds. The transition probabilities of the mode jumps are considered to be partially known, which relax the traditional assumption in Markov jump systems that all of them must be completely known a priori. Following the recent study on the class of systems, a monotonicity is further observed in concern of the conservatism of obtaining the maximal delay range due to the unknown elements in the transition probability matrix. Sufficient conditions for stochastic stability of the underlying systems are derived via the linear matrix inequality (LMI) formulation, and the design of the stabilizing controller is further given. A numerical example is used to illustrate the developed theory.

This paper is concerned with scheduling of a marketing-production system in which the demand rate changes in accordance with marketing actions. Our goal is to provide illuminating descriptions and insight on the optimal control policies. A basic building-block model involving a single machine is developed. The objective is to choose the rates of production and marketing to maximize the overall profit. Consisting of a pair of hedging points, the optimal policy is attractive in practice because of its simplicity and can be computed by solving algebraic equations. Aiming at obtaining analytic solutions, various control regions of the optimal policy are depicted; the structure of the hedging-point policy is fully analyzed.

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.

This paper studies the problem of control for discrete time delay linear systems with Markovian jump parameters. The system under consideration is subjected to both time-varying norm-bounded parameter uncertainty and unknown time delay in the state, and Markovian jump parameters in all system matrices. We address the problem of robust state feedback control in which both robust stochastic stability and a prescribed H/sub /spl infin// performance are required to be achieved irrespective of the uncertainty and time delay. It is shown that the above problem can be solved if a set of coupled linear matrix inequalities has a solution.

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.