Robust control synthesis for discrete-time uncertain semi-Markov jump systems

Abstract

This paper studies the control synthesis for uncertain semi-Markov jump systems in a discrete-time domain subjected to external disturbance. The switching between modes is determined by a function of the transition probability and the sojourn-time distribution between two neighbouring modes. Based on the σ-error mean square stability criterion, time-varying controllers are designed to stabilise the system. By constructing a holding time dependent Lyapunov function, time-varying state-feedback controllers are obtained that meet a set of sufficient conditions in the form of linear matrix inequalities. Two examples, including a DC motor system, are presented to show the validity of the proposed control scheme.

Keywords:

• Semi-Markov jump system
• parameter uncertainty
• $H_{\mathrm{\infty }}$ performance index

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Yueyuan Zhang http://orcid.org/0000-0001-5131-7460

Additional information

Funding

This work was supported by The National Natural Science Foundation of China [61833007, 61773183], The Australia Research Council [DPI 70102644], the 111 Project [B12018] and the National First-class Discipline Program of Light Industry Technology and Engineering [LITE2018-25].

Notes on contributors

Yueyuan Zhang

Yueyuan Zhang received the B.S. degree in control science and engineering from Jiangnan University, Wuxi, China, in 2013. From 2016 to 2018, she was a visiting student with the School of Electrical and Electronic Engineering, University of Adelaide, SA, Australia. Currently, she is a Ph.D. student in control science and engineering from Jiangnan University, Wuxi, China. Her research interest covers stochastic semi-Markov jump systems, control theory and application, model predictive control, event-triggered control scheme, robust control, etc.

Cheng-Chew Lim

Cheng-Chew Lim received his B.Sc. degree (with honors) in Electronic and Electrical Engineering, and his Ph.D. degree from Loughborough University, Leicestershire, U.K. He is now a Professor in Electrical & Electronic Engineering, the University of Adelaide, Australia. His research interests are in the areas of systems and control, wireless communications and optimisation techniques and applications. He is serving as an editorial board member for the Journal of Industrial and Management Optimization, and has served as guest editor of a number of journals, including Discrete and Continuous Dynamical System-Series B, and the Chair of the IEEE Chapter on Control and Aerospace Electronic Systems at the IEEE South Australia Section.

Fei Liu

Fei Liu (M'87) received the B.S. degree in electrical technology and the M.Sc. degree in industrial automation from Wuxi Institute of Light Industry, Wuxi, China, in 1987 and 1990, respectively, and the Ph.D. degree in control science and control engineering from Zhejiang University, Hangzhou, China, in 2002. From 1990 to 1999, he was an Assistant, a Lecturer, and an Associate Professor with Wuxi Institute of Light Industry. Since 2003, he has been a Professor with the Institute of Automation, Jiangnan University, Wuxi. From 2005 to 2006, he was a Visiting Professor with the University of Manchester, Manchester, U.K. His research interests include advanced control theory and application, batch process control engineering, statistical monitoring and diagnosis in industrial process, and intelligent technique with emphasis on fuzzy and neural systems.