Abstract

In this paper, stability properties for discrete-time dynamical systems with set-valued states are studied. We use previous results on detectability and invariance properties to present an extension of Krasovskii and Lyapunov stability results for set dynamical systems, under the assumption of outer semicontinuity of the set-valued maps that define the system's dynamics. We also propose a formulation for closed loop control systems with state-feedback, within the framework of set dynamical systems. Examples illustrate the results.