New Results on Stability and Stabilization of Markovian Jump Systems with Time Delay

Hongwei Xia,Changhong Wang,Yanmin Wang,Li Li,Guangcheng Ma

doi:10.1155/2014/927316

Hongwei Xia, Changhong Wang + Show 3 more

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https://doi.org/10.1155/2014/927316

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Abstract

This technical paper deals with the problem of stochastic stability and stabilization for a class of linear Markovian jumping systems with discrete time-varying delay. A novel delay-dependent stochastic stability criterion for Markovian delay systems is established based on new augmented Lyapunov-Krasovskii functional and delay fractioning techniques. Then a state feedback controller is designed to guarantee the stochastic stability of the resulting closed-loop system. Numerical examples are provided to illustrate the effectiveness of the proposed design approach in this paper.

Highlights

Markovian jump systems are a special class of hybrid systems with both modes and state variables
Since many dynamical systems such as the chemical processes, transportation systems, and manufacturing systems can be modeled as Markovian jump systems, considerable attention has been devoted to the problem of analysis and synthesis for Markovian jump systems over the past decades; see, for example, [1,2,3,4] and the references therein
The information of delay is included in some criteria, which is so-called delay dependent, while others are irrelevant to the delay [15,16,17], which is called delay independent

Summary

Introduction

Markovian jump systems are a special class of hybrid systems with both modes and state variables. Wu et al [20] and He et al [21] tried to seek the relationship between the terms in the Newton-Leibniz formula and to introduce some free weighting matrices to express this relationship and some delay-dependent stability conditions with less conservativeness have been established These methods are quite different from the conventional one of using model transformation which may introduce some superfluous dynamics into the original system. In [24], by choosing an augmented Lyapunov-Krasovskii functional and utilizing the delay-partitioning method, novel delay-dependent mean square asymptotic stability conditions are derived in terms of LMIs. With the idea of delay partitioning, in [25] a new delaydependent stochastic stability criterion on the stochastic stability of Markovian jump systems with time-delay has been proposed, which is less conservative than most existing results. If their dimensions are not explicitly stated, are assumed to be compatible for algebraic operations

Problem Formulations and Preliminaries

Main Results

Numerical Examples

Conclusion