Analysis and synthesis of neural networks with lower block triangular interconnecting structure

A qualitative analysis of Hopfield-type neural network models with lower block triangular interconnecting structure is presented. Such networks are viewed as interconnected systems and the 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. The results address the stability properties of equilibrium points and estimates of trajectory properties. A design method is devised for this class of neural networks to establish desired relationships between scalar-valued analog input signals and output signals in binary form. The applicability of the design methodology is demonstrated 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 resister tolerancer. Specific simulations show that the present design method offers significant improvements over other design techniques that employ Hopfield neural networks