Stability analysis of differential inclusions in Banach space with applications to nonlinear systems with time delays

Abstract

We present new stability results for dynamical systems determined by a class of differential inclusions on Banach space. One of the results shows that under reasonable conditions, the same Lyapunov function can be used in analyzing the stability properties of a given differential inclusion and the stability properties of its convexification. We also establish a result for differential inclusions which is analogous to invariance theory type results for differential equations. To demonstrate applicability, we use the above results in the analysis of the absolute stability problem of regulator systems with multinonlinearities and time delays. Also, we apply the above results in the stability analysis of operating points (equilibria) of a class of integrated circuits with time delays, with an emphasis on a class of artificial neural networks for associative memories. In the applications, we reduce the stability problem of some given nonlinear systems with time delays to the stability problem of a finite number of linear systems with time delays.