On global stability of Hopfield neural networks with discontinuous neuron activations

The paper introduces a general class of neural networks where the neuron activations are modeled, by discontinuous functions. The neural networks have an additive interconnecting structure and they include as particular cases the Hopfield neural networks (HNNs), and the standard Cellular Neural Networks (CNNs), in the limiting situation where the HNNs and CNNs possess neurons with infinite gain. Conditions are obtained which ensure global convergence toward the unique equilibrium point in finite time, where the convergence time can be easily estimated on the basis of the relevant neural network parameters. These conditions are based on the concept of Lyapunov Diagonally Stable (LDS) neuron interconnection matrices, and are applicable to general non-symmetric neural networks.