Stability Analysis of Retarded Differential Inclusions

Abstract

Retarded differential inclusions have drawn more and more attention, due to the development of feedback control systems with delays and dynamical systems determined by retarded differential equations with a discontinuous right-hand side. The purpose of this paper is to establish a result on the stability and asymptotical stability for retarded differential inclusions. Comparing with the previous results, the main result obtained in this paper allows Lyapunov functions to be nonsmooth. Moreover, to deal with the asymptotical stability, it is not required that Lyapunov functions should have an infinitesimal upper limit, but this condition is needed in most of the previous results. To demonstrate applicability, we use the main result in the analysis of asymptotical stability of a class of neural networks with discontinuous activations and delays.