Almost sure stability for a class of dual switching linear discrete‐time systems. (12th January 2020)

• Record Type: Journal Article
• Authors: Long, Fei; Liu, Cai; Ou, Weihua
• Is Part Of: Concurrency and computation. Volume 33:Number 15(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2020-01-12
• Subjects: dual switching -- exponentially almost sure stability -- persistent dwell time -- stochastic multi‐Lyapunov function; Parallel processing (Electronic computers) -- Periodicals; Parallel computers -- Periodicals; 004.35
• DOI: 10.1002/cpe.5666
• Languages: English
• ISSNs: 1532-0626

Abstract

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.