Summary
In this paper, a dual switching discrete‐time linear system, simultaneously subject to deterministic switching and Markov chain, is considered. This study does not consider the transition probability of the Markov chain as fixed but determined by the current position of deterministic switching. Namely, such dual switching discrete‐time linear system is composed of a family of discrete‐time Markov jump systems and follows a rule that directs the switching sequences between them. The exponentially almost sure stability problem, for dual switching discrete‐time linear system with exponential uncertainty, is addressed by using persistent dwell time and stochastic multi‐Lyapunov function. The sufficient conditions for the exponentially almost sure stability of dual switching discrete‐time linear system are expressed as linear matrix inequalities. Finally, a simulation example demonstrates the validity of the derived 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.