Finite-time H∞ control for a class of discrete-time Markovian jump systems with partly unknown time-varying transition probabilities subject to average dwell time switching

• Published in: International journal of systems science Vol. 46; no. 6; pp. 1080 - 1093
• Main Authors: Cheng, Jun, Zhu, Hong, Zhong, Shouming, Zhang, Yuping, Li, Yuanyuan
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 26.04.2015
• Subjects: average dwell time; control; finite-time stability; Markov jump systems; time-varying transition probabilities
• ISSN: 0020-7721; 1464-5319
• DOI: 10.1080/00207721.2013.808716

An extension of a fixed transition probability (TP) Markovian switching model to combine time-varying TPs has offered another set of useful regime-switching models. This paper is concerned with the problem of finite-time H ∞ control for a class of discrete-time Markovian jump systems with partly unknown time-varying TPs subject to average dwell time switching. The so-called time-varying TPs mean that the TPs are varying but invariant within an interval. The variation of the TPs considered here is subject to a class of slow switching signal. Based on selecting the appropriate Lyapunov-Krasovskii functional, sufficient conditions of finite-time boundedness of Markovian jump systems are derived and the system trajectory stays within a prescribed bound. Finally, an example is given to illustrate the efficiency of the proposed method.