A new stability criterion for bidirectional associative memory neural networks of neutral-type

Abstract

In the paper, the global asymptotic stability of equilibrium is considered for continuous bidirectional associative memory (BAM) neural networks of neutral type by using the Lyapunov method. A new stability criterion is derived in terms of linear matrix inequality (LMI) to ascertain the global asymptotic stability of the BAM. The LMI can be solved easily by various convex optimization algorithms. A numerical example is illustrated to verify our result.

Introduction

Since cellular neural networks have been introduced by Chua and Yang [1], extensive research on neural networks has been done by many scientists over the past years [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13]. Also, it is well known that a series of neural networks related to bidirectional associative memory (BAM) models have been proposed by Kosko [14], [15]. These models generalized the single-layer autoassociative Hebbian correlator to a two-layer pattern-matched heteroassociative circuit. This class of networks has been successfully applied to pattern recognition and artificial intelligence. Therefore, the BAM neural networks have been one of the most interesting research topics and have attracted the attention of many researchers [16], [17], [18], [19], [20]. Furthermore, since time delay will inevitably occur in the communication and response of neurons owing to the unavoidable finite switching speed of amplifiers in the electronic implementation of analog neural networks, so it is more in accordance with this fact to study the BAM neural networks with time delays. With regard to recent works, see [21], [22] and the references cited therein. On the other hand, due to the complicated dynamic properties of the neural cells in the real world, the existing neural network models in many cases cannot characterize the properties of a neural reaction process precisely. It is natural and important that systems will contain some information about the derivative of the past state to further describe and model the dynamics for such complex neural reactions [23]. However, the stability analysis of neural networks of neutral-type has been investigated by only a few researchers [23], [24], [25].

Motivated by the above statement, this paper considers asymptotic stability for BAM neural networks of neutral type for the first time. Based on the Lyapunov theory, a new stability criterion is given in terms of LMI. The advantage of the proposed approach is that resulting stability criterion can be performed efficiently via existing numerical convex optimization algorithms such as the interior-point algorithms for solving the linear matrix inequality inequalities [27].

Throughout the paper, a real symmetric matrix P > 0 (⩾0) denotes the matrix P being a positive definite (positive semidefinite) matrix. I denotes the identity matrix of appropriate dimension.