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 closedloop control systems with state-feedback, within the framework of set dynamical systems. Examples illustrate the results.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.