ANALYSIS AND SYNTHESIS OF NEURAL NETWORKS WITH LOWER BLOCK TRIANGULAR INTERCONNECTING STRUCTURE

We conduct a qualitative analysis of Hopfield-type neural network models with lower block triangular interconnecting structure. In our approach we view such networks as interconnected systems and our results are phrased in terms of the qualitative properties of the subsystems of the networks and in terms of the properties of the interconnecting structure of the networks. Our results address the stability properties of equilibrium points and estimates of trajectory properties (e.g., rates of convergence of solutions to asymptotically stable equilibria). The above results enable us to devise a design method for the class of neural networks considered herein to establish desired relationships between scalar-valued analog input signals and output signals in binary form. We demonstrate the applicability of the design methodology advanced herein by means of several specific examples, including the design of an A/D converter, the design of a resistor sorter, and the design of a resistor tolerancer. By means of specific simulations, we demonstrate that the present design method offers significant improvements over existing design techniques that employ Hopfield neural networks. © 1990 IEEE