Globally Asymptotic Stability of Stochastic Nonlinear Systems with Time-Varying Delays via Output Feedback Control

Mingzhu Song,Quanxin Zhu,Hui Wang,Wenwen Cheng,Hongwei Zhou

doi:10.1155/2016/7548156

Abstract

We address the problem of globally asymptotic stability for a class of stochastic nonlinear systems with time-varying delays. By the backstepping method and Lyapunov theory, we design a linear output feedback controller recursively based on the observable linearization for a class of stochastic nonlinear systems with time-varying delays to guarantee that the closed-loop system is globally asymptotically stable in probability. In particular, we extend the deterministic nonlinear system to stochastic nonlinear systems with time-varying delays. Finally, an example and its simulations are given to illustrate the theoretical results.

Highlights

In recent years, the stochastic nonlinear system has received much attention and has enjoyed a good development, which has been widely applied in many fields such as engineering and finance [1]
Since the backstepping method has been introduced in the nonlinear system, the theory of stochastic nonlinear systems has achieved a remarkable development
The other is that Deng and Krstic [7,8,9,10] used a quartic Lyapunov function to guarantee that the closed-loop system is globally asymptotically stable in probability

Summary

Introduction

The stochastic nonlinear system has received much attention and has enjoyed a good development, which has been widely applied in many fields such as engineering and finance [1]. The other is that Deng and Krstic [7,8,9,10] used a quartic Lyapunov function to guarantee that the closed-loop system is globally asymptotically stable in probability Based on their works, Liu et al [11,12,13] employed the quartic Lyapunov function to design the output feedback control for stochastic nonlinear systems. We extend the results of the deterministic nonlinear systems in [21] to the stochastic nonlinear systems with time-varying delays by output feedback control and design a Lyapunov-Krasovskii functional to prove the globally asymptotic stability of the closed-system via the linear observer.

Preliminaries

The Output Feedback Model and Control Design

An Example

Conclusion