BIBO Stabilization of Discrete-Time Stochastic Control Systems with Mixed Delays and Nonlinear Perturbations

Xia Zhou,Yong Ren,Shouming Zhong

doi:10.1155/2013/916357

Abstract

The problem of bounded-input bounded-output (BIBO) stabilization in mean square for a class of discrete-time stochastic control systems with mixed time-varying delays and nonlinear perturbations is investigated. Some novel delay-dependent stability conditions for the previously mentioned system are established by constructing a novel Lyapunov-Krasovskii function. These conditions are expressed in the forms of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using MATLAB LMI Toolbox. Finally, a numerical example is given to illustrate the validity of the obtained results.

Highlights

Many dynamical systems depend on the present states and involve the past ones, generally called the timedelay systems
Motivated by the aforementioned works, in this paper, we investigate BIBO stabilization in mean square for a class of discrete-time stochastic control systems with mixed timevarying delays and nonlinear perturbations
We have derived some conditions for the BIBO stabilization in mean square for a class of discretetime stochastic control systems with mixed time-varying delays

Summary

Introduction

Many dynamical systems depend on the present states and involve the past ones, generally called the timedelay systems. To the best of our knowledge, there is no Abstract and Applied Analysis work reported on the mean square BIBO stabilization for the discrete-time stochastic control systems with mixed timevarying delays. In [33], the midpoint in the time delay’s variation interval is introduced, and the variation interval is divided into two subintervals with equal length, by constructing the Lyapunov functional which involved midpoint to reduce the conservatism of stability conditions This method was first proposed to study the stability and stabilization problems for linear continuous-time systems, and many successful applications were found in [13,14,15]. Motivated by the aforementioned works, in this paper, we investigate BIBO stabilization in mean square for a class of discrete-time stochastic control systems with mixed timevarying delays and nonlinear perturbations.

Notations and Problem Formulation

An Example

Conclusions