Stability of non-instantaneous impulsive systems in Hilbert spaces

Abstract

In this paper, we introduce the concepts of Lyapunov exponent and Lyapunov regularity in Hilbert spaces, which is similar to that in the classical theory. As an application, under sufficiently small perturbations, we establish the asymptotic stability of the zero solution of non-instantaneous impulses nonautonomous nonlinear perturbations systems, which linear system is Lyapunov regular.