Delay-Dependent Robust Exponential Stability for Uncertain Neutral Stochastic Systems with Interval Time-Varying Delay

Weihua Mao,Anhua Wan,Feiqi Deng

doi:10.1155/2012/593780

Abstract

This paper discusses the mean-square exponential stability of uncertain neutral linear stochastic systems with interval time-varying delays. A new augmented Lyapunov-Krasovskii functional (LKF) has been constructed to derive improved delay-dependent robust mean-square exponential stability criteria, which are forms of linear matrix inequalities (LMIs). By free-weight matrices method, the usual restriction that the stability conditions only bear slow-varying derivative of the delay is removed. Finally, numerical examples are provided to illustrate the effectiveness of the proposed method.

Highlights

Numerical examples are provided to illustrate the effectiveness of the proposed method. Dynamical systems, such as the distributed networks, electric power systems, and communication systems, can be efficiently modeled by neutral stochastic functional differential equations, which have been extensively studied in recent years, see 1–8 and references therein
Sufficient conditions on stability of time delay systems are divided into two categories: delay-dependent and delay-independent cases
This paper focuses on the stability analysis of uncertain neutral stochastic distributed system with interval time-varying delay

Summary

Introduction

Dynamical systems, such as the distributed networks, electric power systems, and communication systems, can be efficiently modeled by neutral stochastic functional differential equations, which have been extensively studied in recent years, see 1–8 and references therein. Increasing attention has been focused on delay-dependent stability analysis of delay systems in recent years, see 1–25. The mean-square exponential stability was studied for neutral stochastic systems with fixed delays in 2, 3. Improved delay-dependent robust stability criteria of uncertain stochastic systems with interval time-varying delay were proposed in 12. Few works on the robust delay-dependent exponential stability analysis have been reported for uncertain neutral stochastic distributed system with fast-varying interval time-varying delay. This paper focuses on the stability analysis of uncertain neutral stochastic distributed system with interval time-varying delay. By Lyapunov-Krasovskii functional theory and free-weighting matrices method, a new delaydependent mean-square exponential stability criterion is formulated in terms of LMI, and the usual restriction of τt < 1 is removed. ; Rn be the family of all F0-measurable {φ θ : −τ θ 0}

ΔB1 t x tτ

Main Results

ST2 S2

Numerical Examples

Conclusion