Robust finite-time control for a class of extended stochastic switching systems

Abstract

This article proposes a new design approach for robust finite-time H _∞ control of a class of Markov jump systems with partially known information on the transition jump rates. The system under consideration involves norm-bounded parameter uncertainties and external disturbance. The problems of robust finite-time boundedness and finite-time stabilisation of the underlying systems are considered. Then, a H _∞ state feedback controller is designed. Sufficient conditions that consider only the known bounds on the transition jump rates are developed in the form of linear matrix inequalities. A numerical example is included to show the usefulness of the theoretic results obtained.

Keywords:

• Markov jump systems
• unknown jump rates
• finite-time boundedness
• finite-time stabilisation
• H _∞ control

Acknowledgements

We thank the reviewers for their valuable comments and suggestions which have improved the presentation of the article. This work was partially supported by the National Natural Science Foundation of China (Grant No. 60974001), the Programme for New Century Excellent Talents in University (Grant No. 050485), the Programme for Innovative Research Team of Jiangnan University and the Engineering and Physical Sciences Research Council, UK (EP/F029195).