Global exponential stability analysis of discrete-time BAM neural networks with delays: A mathematical induction approach

Abstract

The problem of global exponential stability analysis for discrete-time bidirectional associative memory (BAM) neural networks with time-varying delays is investigated. By using the mathematical induction method, a novel exponential stability criterion in the form of linear matrix inequalities is firstly established. Then stability criteria depending upon only the system parameters are derived, which can easily checked by using the standard toolbox software (e.g., MATLAB). The proposed approach is directly based on the definition of global exponential stability, and it does not involve the construct of any Lyapunov–Krasovskii functional or auxiliary function. For a class of special cases, it is theoretical proven that the less conservative stability criteria can be obtained by using the proposed approach than ones in literature. Moreover, several numerical examples are also provided to demonstrate the effectiveness of the proposed method.