Discrete-Time Interval Bidirectional Associative Memories - Novel Stability Results

Abstract

This paper develops the analysis of a special type of asymptotic stability, called componentwise asymptotic stability (CWAS), for discrete-time Bidirectional Associative Memory (BAM) neural networks with interval type parameters. Unlike the standard notion of asymptotic stability, that gives global information on the state-space vector, expressed in terms of arbitrary norms, CWAS allows an individual monitoring of each state-space variable approaching the equilibrium point. At conceptual level, CWAS brings a refinement in the stability theory by revealing the existence of positive invariant time-dependent rectangular sets with respect to the state space trajectories. Our results provide sufficient conditions for testing the CWAS of BAMs with interval type parameters relying on the Schur stability of a matrix which is adequately built from the intervals expressing the parameter uncertainties.