Asymptotic Stability of autonomous and Non-Autonomous Discrete Linear Inclusions

The article is devoted to the study of absolute asymptotic stability of discrete linear inclusions (both autonomous and non-autonomous) in Banach space. We establish the relation between absolute asymptotic stability, uniform asymptotic stability and uniform exponential stability. It is proved that for compact (completely continuous) discrete linear inclusions these notions of stability are equivalent. We study this problem in the framework of non-autonomous dynamical systems (cocyles).