Stability and stabilisation of Markovian jump systems under fast switching: an averaging approach

Guoliang WangSchool of Information and Control Engineering, Liaoning Petrochemical University, Fushun, Liaoning, People's Republic of ChinaCorrespondence[email protected] [email protected]

https://orcid.org/0000-0003-3236-2404 View further author information

Yande ZhangSchool of Information and Control Engineering, Liaoning Petrochemical University, Fushun, Liaoning, People's Republic of ChinaView further author information

Yunshuai RenSchool of Information and Control Engineering, Liaoning Petrochemical University, Fushun, Liaoning, People's Republic of ChinaView further author information

Abstract

This paper addresses the problems of stability and stabilisation of Markovian jump systems (MJSs) with fast switching. First, a novel model by applying an averaging approach to the fast switching is proposed. Then, a new method for constructing an auxiliary system is given to make the stability analysis. It is proved that the stability of the originally fast switching MJS could be guaranteed by an MJS with an average switching, if the fast switching achieves its average approximation sufficiently fast. Based on the proposed results, some extensions about generally stabilising controllers are considered, where the fault-tolerant situation is involved too. All the conditions are presented in terms of LMIs. Finally, two numerical examples are used to demonstrate the effectiveness and superiority of the method.

Keywords:

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Open Project of Key Field Alliance of Liaoning Province [grant number 2022-KF-11-03].

Notes on contributors

Guoliang Wang

Guoliang Wang was born in Weifang, Shandong, China, in 1981. He is presently a professor in the department of automation, Liaoning Petrochemical University. His research interests include Markovian jump systems, singular systems and stochastic control.

Yande Zhang

Yande Zhang was born in Wuwei, Gansu, China, in 1996. He is now a master in the department of automation, Liaoning Petrochemical University, Fushun, Liaoning, China. His research interest is Markovian jump systems.

Yunshuai Ren

Yunshuai Ren was born in Zibo, Shandong, China, in 1995. He is now a master in the department of automation, Liaoning Petrochemical University, Fushun, Liaoning, China. His research interest is semi-Markovian jump systems.

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