Stability Analysis for Discrete-Time Stochastic Fuzzy Neural Networks with Mixed Delays

Yajun Li,Quanxin Zhu

doi:10.1155/2019/8529053

Abstract

This paper is concerned with the stability problem of a class of discrete-time stochastic fuzzy neural networks with mixed delays. New Lyapunov-Krasovskii functions are proposed and free weight matrices are introduced. The novel sufficient conditions for the stability of discrete-time stochastic fuzzy neural networks with mixed delays are established in terms of linear matrix inequalities (LMIs). Finally, numerical examples are given to illustrate the effectiveness and benefits of the proposed method.

Highlights

Such applications of neural networks heavily depend on the dynamical behaviors of the networks
The main task of the neural networks designers is to ensure the stability of the equilibrium point of the designed system
Motivated by the above discussion, in this paper we investigate the stability problem for a class of discrete-time stochastic fuzzy neural networks system with mixed timevarying delays

Summary

Introduction

Such applications of neural networks heavily depend on the dynamical behaviors of the networks. The stability and passivity problem for stochastic neural networks with different time-delays were investigated widely, and many important results were reported (see, e.g., [24–37] and references therein). In [42], by utilizing the inequality technic and freeweighting matrices, constructing novel Lyapunov functions, some new results about the robust exponential stability issue of the fuzzy uncertain neural networks were obtained, but adding on the free weight matrices methods has increased computation load and the conservatism of system. Mathematical Problems in Engineering square exponential stability of the fuzzy neural networks with mixed delays was studied, but time-delay was only the constant one, which is not practical in the real applications. Motivated by the above discussion, in this paper we investigate the stability problem for a class of discrete-time stochastic fuzzy neural networks system with mixed timevarying delays. E{⋅} stands for the mathematical expectation operator with respect to the given probability measure P

Problem Description

Main Results

Numerical Examples

Conclusions