Almost sure estimation and synthesis of ultimate bounds for discrete-time Markov jump linear systems

ABSTRACT

This paper is concerned with the problems of almost sure ultimate bound estimation and controller design for Markov jump linear systems with bounded stochastic disturbances. By utilising a Lyapunov-based scheme proposed in this paper, an almost sure estimation of ellipsoidal ultimate bound (EUB) of the system is obtained through tractable matrix inequalities. On the basis of the estimation results, the problem of designing mode-dependent state feedback controllers that make the closed-loop system admit a prescribed ellipsoid as an EUB is considered. The obtained results on estimation and synthesis are then extended to the case of systems with deficient mode information. Finally, a practical example in DC motor devices is presented to demonstrate the applicability of the obtained results.

KEYWORDS:

• Almost sure stability
• ultimate bound estimation
• Markov jump systems
• LMIs

Acknowledgments

The authors would like to thank the Editor(s) and anonymous Reviewers for their constructive comments and suggestions that have helped to improve the present paper.

Disclosure statement

No potential conflict of interest was reported by the authors.