Robust Stability, Stabilization, andH∞Control of a Class of Nonlinear Discrete Time Stochastic Systems

Xiushan Jiang,Weihai Zhang,Yu-Hong Wang,Tianliang Zhang

doi:10.1155/2016/5185784

Abstract

This paper studies robust stability, stabilization, andH∞control for a class of nonlinear discrete time stochastic systems. Firstly, the easily testing criteria for stochastic stability and stochastic stabilizability are obtained via linear matrix inequalities (LMIs). Then a robustH∞state feedback controller is designed such that the concerned system not only is internally stochastically stabilizable but also satisfies robustH∞performance. Moreover, the previous results of the nonlinearly perturbed discrete stochastic system are generalized to the system with state, control, and external disturbance dependent noise simultaneously. Two numerical examples are given to illustrate the effectiveness of the proposed results.

Highlights

Stochastic control has been one of the most important research topics in modern control theory
This paper studies robust stability, stabilization, and H∞ control for a class of nonlinear discrete time stochastic systems
H∞ control is one of the most important robust control approaches, which aims to design the controller to restrain the external disturbance below a given level

Summary

Introduction

Stochastic control has been one of the most important research topics in modern control theory. [21] tried to discuss a general nonlinear H∞ control of discrete time stochastic systems, but only the H∞ control of a class of norm bounded systems was perfectly solved based on linear matrix inequality (LMI) approach. The considered nonlinear dynamic term is priorly unknown but belongs to a class of functions with a bounded energy level, which represent a kind of very important nonlinear functions, and has been studied by many researchers; see, for example, [41] For such a class of nonlinear discrete time stochastic systems, the stochastic stability, stabilization, and H∞ control have been discussed, respectively, and testing criteria have been obtained. Lw (NT, Rn) and ‖y‖lw (N,Rn) can be defined

System Descriptions and Definitions

Main Results

Numerical Examples

Conclusion