Feedback Stabilization for a Class of Nonlinear Stochastic Systems with State- and Control-Dependent Noise

Yu-Hong Wang,Tianliang Zhang,Weihai Zhang

doi:10.1155/2014/484732

Abstract

This paper mainly studies the state feedback stabilizability of a class of nonlinear stochastic systems with state- and control-dependent noise. Some sufficient conditions on local and global state feedback stabilizations are given in linear matrix inequalities (LMIs) and generalized algebraic Riccati equations (GAREs). Some obtained results improve the previous work.

Highlights

Stability and stabilization are two important topics in modern control theory, which are first of considered issues in the systems analysis and synthesis
It is well known that stochastic control has become a very popular research area, which has been applied to mathematical finance [1], quantum systems [2], and so forth; stochastic stability and stabilization have been studied by many researchers; we refer the reader to the celebrated book [1] for the discussions of various stabilities
The study for stabilization of nonlinear stochastic systems has attracted great attention; the methods appearring in studying this topic can be summarized as follows: generalized algebraic Riccati equations (GAREs)-based method [9, 12, 18, 19]; control Lyapunov function method [1, 3,4,5,6, 20]; passive system method [21], and spectral analysis method based on generalized Lyapunov operators [13, 16, 17]

Summary

Introduction

Stability and stabilization are two important topics in modern control theory, which are first of considered issues in the systems analysis and synthesis. We refer the reader to [19] for the stabilization of general nonlinear stochastic systems, where a class of new Hamilton-Jacobi inequalities were presented. We deal with a class of linearized systems with both the state- and control-dependent noise. Some sufficient conditions on local state feedback stabilization are given via LMIs and GAREs, respectively, which generalize and improve the results of [18]. We investigate the global state feedback stabilization and a sufficient condition is given in terms of LMIs. A numerical example verifies the effectiveness of our results

Problem Setting

Locally Asymptotic Stabilization

Globally Asymptotic Stabilization

Numerical Example

Conclusion