Asynchronous control of discrete-time stochastic bilinear systems with Markovian switchings

Abstract

This paper is concerned with the problem of asynchronous control for a class of discrete-time Markov systems with multiplicative stochastic white noises. Based on a stability analysis scheme developed from mode-dependent Lyapunov function method, we first derive testable conditions in linear matrix inequality (LMI) setting to ensure the robust stability of the closed-loop system. We then recast the proposed stability conditions into equivalent forms that are later utilised to design a multi-mode asynchronous state-feedback controller (ASFC) that makes the closed-loop system stable. An extension to the case of deficient mode information (i.e. transition rates of the system and the controller are not fully accessible) is also presented. Finally, a model of networked control with DC devices is given to demonstrate the efficacy of the proposed design scheme.

Keywords:

• Asynchronous control
• Markov jump systems
• multiplicative noises
• stochastic stability

Acknowledgments

The authors would like to thank the Editors and Anonymous reviewers for their constructive comments and suggestions that are helpful to improve the present paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Le Van Hien  http://orcid.org/0000-0003-1787-3011

Additional information

Funding

This work was supported by the Hanoi Pedagogical University 2 [grant number C.2017-18-04].