Global Exponential Stability Criteria for Bidirectional Associative Memory Neural Networks with Time-Varying Delays

J Thipcha,P Niamsup

doi:10.1155/2013/576721

Abstract

The global exponential stability for bidirectional associative memory neural networks with time-varying delays is studied. In our study, the lower and upper bounds of the activation functions are allowed to be either positive, negative, or zero. By constructing new and improved Lyapunov-Krasovskii functional and introducing free-weighting matrices, a new and improved delay-dependent exponential stability for BAM neural networks with time-varying delays is derived in the form of linear matrix inequality (LMI). Numerical examples are given to demonstrate that the derived condition is less conservative than some existing results given in the literature.

Highlights

A class of neural networks related to bidirectional associative memory (BAM) has been introduced by Kosko [1]
Throughout this paper, we make the following assumption on the activation function fi(⋅), gj(⋅)
This paper has proposed a new sufficient condition guaranteeing the global exponential stability criteria for bidirectional associative memory neural networks with timevarying delays and generalized activation functions

Summary

Introduction

A class of neural networks related to bidirectional associative memory (BAM) has been introduced by Kosko [1]. This model generalized the single-layer autoassociative Hebbian correlator to a two-layer pattern-matched heteroassociative circuit. In [14, 15, 18, 20–22, 24– 27], several sufficient conditions on the global exponential stability of BAM neural networks with time-varying delays have been derived. With a properly designed Lyapunov-Krasovskii functional as well as introducing free-weighting matrices, one may derive stability criteria in term of linear matrix inequality (LMI) which is solved by several available algorithms. Based on the above discussion, we propose to study the problem of global exponential stability of BAM neural networks with time-varying delays and generalized activation functions. For symmetric matrices X and Y, the notation X > Y (resp., X ≥ Y) means that the matrix X − Y is positive definite (resp., nonnegative). λm(⋅) and λM(⋅) denote the smallest and largest eigenvalue of given square matrix, respectively

Model Description and Preliminaries

Main Result

Numerical Examples

Conclusion