Global Exponential Stability Conditions for Discrete-Time BAM Neural Networks Affected by Impulses and Time-Varying Delays.

This paper studies global exponential stability (GES) of discrete-time (D-T) BAM neural networks (BAMNNs) affected by impulses and time-varying delays. An impulse-free D-T BAMNN with time-varying delays is first developed via the properties of M-matrices, and then the relation between the solutions of the original and new BAMNNs is established. From which, sufficient conditions for GES of the original BAMNN are derived by investigating GES conditions of the new BAMNN based on the counter-evidence and the nature of the nonsingular M-matrix. The results of illustrative examples show that the obtained GES criteria are effective. By comparing with previous results, this paper has the following three merits: (a) the obtained GES criteria are to check the positivity of eigenvalues of a constant matrix, which is easy to realize; (b) this method can be used for other D-T system models affected by impulses and time-varying delays; and (c) the numerical results show that our method is less conservative than ones in other literatures. [ABSTRACT FROM AUTHOR]