Event-triggered and self-triggered H_∞ output tracking control for discrete-time linear parameter-varying systems with network-induced delays

Abstract

In this paper, we address the event-triggered and self-triggered $H_{\mathrm{\infty }}$ output tracking problem of discrete LPV systems with network-induced delay. Considering the time delay and external disturbance, we formulate the closed-loop event-triggered output tracking problem into a time-delayed discrete polytopic linear parameter-varying system with relative event-triggering mechanism. Then, by constructing the parameter-dependent Lyapunov–Krasovskii functional, we derive a sufficient condition such that the closed-loop system is global asymptotic stable and satisfies the $H_{\mathrm{\infty }}$ output tracking performance. Further, we develop an approach to design the event-triggering mechanism and $H_{\mathrm{\infty }}$ output tracking controller. The parameters of event-triggering mechanism and the gains of output tracking controller are obtained by solving linear matrix inequalities. Moreover, we extend the results of the event-triggered control to the self-triggered $H_{\mathrm{\infty }}$ output tracking control. This not only mitigates the usage of network bandwidth but also avoids the use of additional hardware. Finally, the numerical simulation is included to illustrate the usefulness and effectiveness of the proposed approach.

Keywords:

• $H_{\mathrm{\infty }}$ output tracking control
• linear parameter-varying system
• networked control system
• event-triggered control
• self-triggered control

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The author is grateful for the financial support of National Natural Science Foundation of China [grant number 60575036] and Natural Science Foundation of Heilongjiang Province [grant number F201222].

Notes on contributors

Jin-jie Huang

Jin-jie Huang received the B.S. and M.S. degrees in Automatic Control from Harbin University of Science and Technology, Harbin, China, in 1990 and 1997, respectively, and the Ph.D. degree in Control Theory and Control Engineering from Harbin Institute of Technology, Harbin, China, in 2004. He is currently a full Professor with the School of Automation and the School of Computer Science and Technology, Harbin University of Science and Technology, Harbin, China. His research interests include linear system control, network control system, nonlinear control system.

Xiao-zhen Pan

Xiao-zhen Pan received the B.S. and M.S. degrees in Automatic Control from Harbin University of Science and Technology, Harbin, China, in 2014 and 2017, respectively, where she is currently working towards his Ph.D. degree in Harbin University of Science and Technology. Her research interests include event-triggered control, robust control, and LPV system.

Xian-zhi Hao

Xian-zhi Hao received the B.S. and M.S. degrees in Automatic Control from Harbin University of Science and Technology, Harbin, China, in 2015 and 2017, respectively, where he is currently working towards his Ph.D. degree in Harbin University of Science and Technology. His research interests include switching control, robust control, switched system and positive linear system.