Further results on H_∞ control for discrete-time Markovian jump time-delay systems

ABSTRACT

This paper studies the problem of H_∞ control for a class of discrete-time Markovian jump systems with time delay. The purpose is to improve the existing results on H_∞ controller design for Markovian jump systems. A novel summation inequality is presented and an improved stability criterion for the system is derived by utilising the new inequality, which is proved to be less conservative than most results in the literature. Then the state feedback controller is designed, which guarantees the stochastic stability of the closed-loop system with a given disturbance attenuation. Numerical examples are provided to illustrate the effectiveness and advantages of the proposed techniques.

KEYWORDS:

• Discrete-time Markovian jump system
• time delay
• stochastic stability
• H_∞ control

Acknowledgement

The authors would like to thank the associate editor and the referees for their very helpful comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research is partially supported by the National Natural Science Foundation of China [grant number 61503094], the Fundamental Research Funds for the Central Universities and China Postdoctoral Science Foundation [grant number 2015M570292, 2016T90290, & LBH-Z14091].