Analysis and synthesis techniques for Hopfield type synchronous discrete time neural networks with application to associative memory

A qualitative theory for synchronous discrete time Hopfield-type neural networks is established. The authors´ objectives are accomplished in two phases. First, they address the analysis of the class of neural networks considered. Next, making use of these results, they develop a synthesis procedure for the class of neural networks considered. In the analysis section, techniques from the theory of large-scale interconnected dynamical systems are used to derive tests for the asymptotic stability of an equilibrium of the neural network. Estimates for the rate at which the trajectories of the network will converge from an initial condition to a final state are presented. In the synthesis section the stability tests from the analysis section are used as constraints to develop a design algorithm for associative memories. The algorithm presented guarantees that each desired memory will be stored as an equilibrium, and that each desired memory will be asymptotically stable. The applicability of these results is demonstrated by means of two specific examples