Passivity and passification for switching Markovian jump systems with time-varying delay and generally uncertain transition rates

• Published in: IET control theory & applications Vol. 10; no. 15; pp. 1944 - 1955
• Main Authors: Qi, Wenhai, Gao, Xianwen, Kao, Yonggui
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 10.10.2016
• Subjects: Brief Paper; control system synthesis; controller design method; Controllers; Delay; delays; Design engineering; Dwell time; dwell time switching; exponential mean‐square stability; generally uncertain transition rates; least mean squares methods; linear matrix inequalities; Linear systems; Markov processes; Markovian jump linear systems; passification; Passivity; piecewise‐constant transition rate matrix; stabilising controller; stability; stochastic passivity; sufficient conditions; Switching; switching Markovian jump systems; time‐varying delay; time‐varying system; time‐varying systems; piecewise-constant transition rate matrix; time-varying systems; least mean squares methods; time-varying delay; Markovian jump linear systems; controller design method; control system synthesis; time-varying system; switching Markovian jump systems; stabilising controller; sufficient conditions; linear matrix inequalities; delays; Markov processes; dwell time switching; exponential mean-square stability; passivity; passification; stability; generally uncertain transition rates; stochastic passivity
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/iet-cta.2015.0726

This study deals with the problem of passivity and passification for switching Markovian jump systems with time-varying delay and generally uncertain transition rates. The considered systems could be viewed as Markovian jump linear systems governed by a piecewise-constant transition rate matrix, which is subject to a high level average dwell time switching. The time delay is considered as time-varying and meets the requirements of the upper and lower bounds. The generally uncertain transition rates cover uncertain transition rates and partly known transition rates as two special cases. First, sufficient conditions, which guarantee the exponential mean-square stability and stochastic passivity of the underlying systems, are presented by resorting to average dwell time approach. Second, the design of the stabilising controller is given further. Moreover, an improved controller design method, which could provide efficiency and practicability, is further developed. All the proposed conditions are given in the form of linear matrix inequalities. Finally, practical examples illustrate the validity of the obtained results.