Robust extended dissipative control for sampled-data Markov jump systems

Abstract

This paper investigates the problem of the sampled-data extended dissipative control for uncertain Markov jump systems. The systems considered are transformed into Markov jump systems with polytopic uncertainties and sawtooth delays by using an input delay approach. The focus is on the design of a mode-independent sampled-data controller such that the resulting closed-loop system is mean-square exponentially stable with a given decay rate and extended dissipative. A novel exponential stability criterion and an extended dissipativty condition are established by proposing a new integral inequality. The reduced conservatism of the criteria is demonstrated by two numerical examples. Furthermore, a sufficient condition for the existence of a desired mode-independent sampled-data controller is obtained by solving a convex optimisation problem. Finally, a resistance, inductance and capacitance (RLC) series circuit is employed to illustrate the effectiveness of the proposed approach.

Keywords:

• extended dissipative control
• Markov jump systems
• sampled data
• mode-independent controller

Acknowledgements

The authors wish to thank the editor and reviewers for their helpful and constructive comments and suggestions that have helped greatly improve the presentation of the paper.

Additional information

Funding

This work was supported by a 2013 Yeungnam University Research Grant. Also, this work was supported by the National Natural Science Foundation of China [grant number 61304066], [grant number 61304072], [grant number 61021002], [grant number 61322301], [grant number 61104007]; the Natural Science Foundation of Anhui Province [grant number 1308085QF119]; the Key Foundation of Natural Science for Colleges and Universities in Anhui province [grant number KJ2012A049]; the Fundamental Research Funds for the Central Universities, China [grant number HIT.BRETIII.201211], [grant number HIT.BRETIV.201306].