Results concerning the absolute stability of delayed neural networks.

Abstract

We report on results concerning the global asymptotic stability (GAS) and absolute stability (ABST) of delay models of continuous-time neural networks. These results present sufficient conditions for GAS and in case the network has instantaneous signalling as well as delay signalling (for example, a delayed cellular neural network (DCNN)), are milder than previously known criteria; they apply to neural networks with a broad range of activation functions assuming neither differentiability nor strict monotonicity. We are therefore able to interpret the results as guarantees of absolute stability of the network with respect to the wide class of admissible activation functions. Furthermore, these results do not assume symmetry of the connection matrices. We also present a sufficient condition for absolute stability in the presence of nonconstant delays.