Robust stability of nonlinear time-delay systems with applications to neural networks

In the first part of this paper we consider a family of nonlinear time-delay systems with uncertainties. For such systems, we present two types of sufficient conditions for robust stability. One type involves delay independent results while the other type involves delay dependent results. In the second part, we apply these sufficient conditions to a class of time-delay artificial neural networks and obtain practical criteria to test asymptotic stability of the equilibria of these time-delay artificial neural networks, with or without perturbations. These criteria require verification of the definiteness of a certain matrix, or verification of a certain inequality. Our results provide also a method of estimating the domain of attraction of the asymptotically stable equilibria of the time-delay neural networks. The applicability of our results is demonstrated by means of three specific examples.