Stabilization of a class of time-varying systems in Hilbert spaces

Abstract

This paper studies the problem of stabilization of the infinite-dimension time-varying systems in Hilbert space where the associated nominal system is a certain class of linear time-varying systems and the perturbation term satisfies some certain conditions. In contrast to the previous results, the stabilizability conditions are obtained by solving a Ricatti differential equation and do not involve any stability property of the evolution operator. Our goal is to prove the sufficient conditions for the case of uniform exponential stability of the origin. The obtained result extends existing results in the literature to infinite-dimensional and time-varying control systems.