Output Feedback Stabilization and Disturbance Attenuation of Time-Delay Systems with Markovian Jump Parameters

Control and Intelligent Systems 01/2004; 32(3). DOI: 10.2316/Journal.201.2004.3.201-1195
Source: OAI


This article investigates the problems of stochastic stabilization and control for a class of linear time-delay systems with Markovian jump parameters via output feedback. The jumping parameters are modelled as continuous-time, discrete-state Markov process. The delay factor is unknown and time-varying with a known bound. Concepts of weak and strong delay-dependent stochastic stability are introduced, and appropriate criteria applied to the jumping systems are developed. The control objective is to design an output-feedback controller such that stochastic stability and a prescribed H∞-like performance for a closed-loop system are guaranteed. We establish that the stability and stabilization problems for the time-delay Markovian jump systems can be essentially solved in terms of the solutions of a finite set of coupled linear matrix inequalities (LMIs). We show that in the case of weak delay-dependence, the controller is of arbitrary order and the associated gain matrices are computed implicitly. In the case of strong–weak coupling the controller is of full-order and explicit expressions are given for the associated gain matrices.

4 Reads
  • [Show abstract] [Hide abstract]
    ABSTRACT: In this paper, we deal with the problems of mode‐dependent decentralized stability and stabilization with ℋ∞ performance for a class of continuous‐time interconnected jumping time‐delay systems. The jumping parameters are governed by a finite state Markov process and the delays are unknown time‐varying and mode‐dependent within interval. The interactions among subsystems satisfy quadratic bounding constraints. To characterize mode‐dependent local stability behavior, we employ an improved Lyapunov–Krasovskii functional at the subsystem level and express the stability conditions in terms of linear matrix inequalities (LMIs). A class of local decentralized state‐feedback controllers is developed to render the closed‐loop interconnected jumping system stochastically stable. Then, we extend the feedback strategy to dynamic observer‐based control and establish the stochastic stabilization via LMIs. It has been established that the developed results encompass several existing results as special cases which are illustrated by simulation of examples. Copyright © 2011 John Wiley & Sons, Ltd.
    International Journal of Robust and Nonlinear Control 05/2012; 22(7). DOI:10.1002/rnc.1736 · 3.18 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: Although stochastic dynamical systems have received a great deal of attention in terms of stabilization studies, so far there are few works on controlled stochastic dynamical systems with state delay. In this paper, a controlled stochastic dynamical system represented by a stochastic differential equation with state delay is considered. Condition under which the system is exponentially stable in mean square and in probability is examined.
    Systems & Control Letters 06/2014; 68(1):95–100. DOI:10.1016/j.sysconle.2014.03.008 · 2.06 Impact Factor