Almost sure stability for a class of dual switching linear discrete‐time systems

• Published in: Concurrency and computation Vol. 33; no. 15
• Main Authors: Long, Fei, Liu, Cai, Ou, Weihua
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc 10.08.2021
• Subjects: Discrete time systems; dual switching; Dwell time; exponentially almost sure stability; Liapunov functions; Linear matrix inequalities; Markov analysis; Markov chains; Mathematical analysis; persistent dwell time; Stability; stochastic multi‐Lyapunov function; Switching sequences; Transition probabilities
• ISSN: 1532-0626; 1532-0634
• DOI: 10.1002/cpe.5666

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.