and Synthesis Techniques for Hopfield Synchronous Discrete Time Neural Networks with Application to Associative Memory
Anthony N. MICHEL, Jay A. Farrell, Hung-Fa Sun · 1990
In the present paper we establish a qualitative theory for synchronous discrete time Hopfield-type neural networks. Our objectives are accomplished in two phases. First, we address the analysis of the class of neural networks considered. Next, making use of these results, we develop a synthesis procedure for the class of neural networks considered herein. In the analysis section, we utilize techniques from the theory of large-scale interconnected dynamical systems to derive tests for the asymptotic stability of an equilibrium of the neural network. We also present estimates for the rate at which the trajectories of the network will converge from an initial condition to a final state. In the synthesis section we utilize the stability tests from the analysis section as con- straints to develop a design algorithm for associative memories. The present algorithm guarantees that each desired memory will be stored as an equilibrium and that each desired memory will be asymptotically stable. The applicability of the present results is demonstrated by means of two specific examples.