Finite‐Time Robust Stabilization for Stochastic Neural Networks

Weixiong Jin,Xiaoyang Liu,Nan Jiang,Xiangjun Zhao,Zhengxin Wang

doi:10.1155/2012/231349

Abstract

This paper is concerned with the finite‐time stabilization for a class of stochastic neural networks (SNNs) with noise perturbations. The purpose of the addressed problem is to design a nonlinear stabilizator which can stabilize the states of neural networks in finite time. Compared with the previous references, a continuous stabilizator is designed to realize such stabilization objective. Based on the recent finite‐time stability theorem of stochastic nonlinear systems, sufficient conditions are established for ensuring the finite‐time stability of the dynamics of SNNs in probability. Then, the gain parameters of the finite‐time controller could be obtained by solving a linear matrix inequality and the robust finite‐time stabilization could also be guaranteed for SNNs with uncertain parameters. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design method.

Highlights

Since the first paper of Ott et al 1, a large number of monographs and papers studying the stabilization of the nonlinear systems without or with delays have been published 2–5
We first give some theorems in detail to guarantee that the original point of SNN 2.6 is stabilized in finite time, that is, the controlled system 2.10 with 2.11 is finitetime stable in probability
We have investigated the issue of finite-time stabilization for SNNs with noise perturbations by constructing a continuous nonlinear stabilizator

Summary

Introduction

Since the first paper of Ott et al 1 , a large number of monographs and papers studying the stabilization of the nonlinear systems without or with delays have been published 2–5 These publications have developed many control techniques including continuous feedback and discontinuous feedback. The robust stability has been studied for neural networks with parameter uncertainties 21–24 or external stochastic perturbations 7, 19, 25,. We will focus on the finite-time robust stabilization for neural networks with both stochastic perturbations and parameter uncertainties. I and 0 represent the identity matrix and a zero matrix, respectively; diag · · · stands for a block-diagonal matrix Matrices, if their dimensions are not explicitly stated, are assumed to be compatible for algebraic operations

Model Formulation and Preliminaries

Main Results

Two Numerical Examples

Conclusions