A constructive method to static output stabilisation of Markov jump systems

Abstract

This paper is concerned with the static output feedback stabilisation of Markov jump systems. Transition probabilities are assumed to be incomplete, namely, they may be known, uncertain with known lower and upper bounds and unknown. To linearise the nonlinearities induced by unknown transition probabilities, a linearisation is developed. To solve the static output feedback problem by means of linear matrix inequalities, a constructive method is proposed to separate the controller gain matrices from Lyapunov variables. Based on the linearisation and the separation, sufficient conditions are established to guarantee that the closed-loop system is stochastically stable by the designed static output feedback controller. The obtained results are further extended to deal with norm-bounded or polytopic uncertainties on system matrices. Numerical examples are given to demonstrate the effectiveness of the proposed method.

Keywords:

• Markov jump system
• static output feedback
• linear matrix inequality

Acknowledgements

The authors would like to thank the editor, the associate editor and the reviewers for their valuable comments and suggestions which help to significantly improve the quality and presentation of this paper.

Disclosure statement

Neither I nor my co-author has a commercial interest, financial interest, and/or other relationship with manufacturers of pharmaceuticals, laboratory supplies, and/or medical devices or with commercial providers of medically related services.

Additional information

Funding

This work is supported in part by the National Natural Science Foundation of China [grant numbers 61273155, 61273119, 61322312, 61403189]; the Natural Science Foundation of Jiangsu Province of China [grant number BK20130949]; the Doctoral Foundation of Ministry of Education of China [grant number 20133221120012]; the Natural Science Foundation of Jiangsu Provincial Universities of China [grant number 13KJB120004]; the Jiangsu Postdoctoral Science Foundation [grant number 1401015B]; New Century Excellent Talents in University [grant number NCET-11-0083]; a Foundation for the Author of National Excellent Doctoral Dissertation of China [grant number 201157].