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Almost sure stability for a class of dual switching linear discrete‐time systems
Author(s) -
Long Fei,
Liu Cai,
Ou Weihua
Publication year - 2020
Publication title -
concurrency and computation: practice and experience
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.309
H-Index - 67
eISSN - 1532-0634
pISSN - 1532-0626
DOI - 10.1002/cpe.5666
Subject(s) - discrete time and continuous time , markov chain , dwell time , mathematics , exponential stability , lyapunov function , control theory (sociology) , linear system , continuous time markov chain , dual (grammatical number) , markov property , computer science , markov model , mathematical analysis , statistics , nonlinear system , control (management) , artificial intelligence , medicine , art , clinical psychology , physics , literature , quantum mechanics
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.