Delay-Dependent Exponential Stability for Uncertain Neutral Stochastic Systems with Mixed Delays and Markovian Jumping Parameters

Huabin Chen

doi:10.1155/2012/748279

Abstract

This paper is mainly concerned with the globally exponential stability in mean square of uncertain neutral stochastic systems with mixed delays and Markovian jumping parameters. The mixed delays are comprised of the discrete interval time-varying delays and the distributed time delays. Taking the stochastic perturbation and Markovian jumping parameters into account, some delay-dependent sufficient conditions for the globally exponential stability in mean square of such systems can be obtained by constructing an appropriate Lyapunov-Krasovskii functional, which are given in the form of linear matrix inequalities (LMIs). The derived criteria are dependent on the upper bound and the lower bound of the time-varying delay and the distributed delay and are therefore less conservative. Two numerical examples are given to illustrate the effectiveness and applicability of our obtained results.

Highlights

It is well known that many dynamical systems depend on the present and past states and involve the derivative with delays as well as the functional of the past history
Some fundamental theories of neutral stochastic delay differential equations are introduced in 1, 8. Since they can be extensively applied into many branches for the control field, the problem about the exponential stability and the asymptotical stability of the neutral stochastic delay systems has attracted many authors’ attention over the past few years, and many less conservative results of delay-dependent conditions ensuring the stabilization analysis and H∞ filtering design for such systems have been reported in many works, see, for example, 9–14 and references therein
Some linear matrix inequalities (LMIs)-based sufficient conditions for the mean-square exponential stability analysis of stochastic systems of neutral type have been obtained by introducing an auxiliary vector in 12

Summary

Introduction

It is well known that many dynamical systems depend on the present and past states and involve the derivative with delays as well as the functional of the past history. Some LMI-based sufficient conditions for the mean-square exponential stability analysis of stochastic systems of neutral type have been obtained by introducing an auxiliary vector in. Kolmanovskii et al in , and Mao et al in have derived the exponential stability of the neutral stochastic delay systems with Markovian jumping parameters, some sufficient conditions obtained by using the estimate method are not checked. By constructing an appropriate Lyapunov functional, some LMIs-based sufficient conditions ensuring the exponential stability in mean square of the uncertain neutral stochastic systems with mixed delays and Markovian jumping parameters are obtained by using the stochastic analysis and some bounding technique.

Problem Formulation

Main Results

Numerical Examples

Conclusions