A multiple convex Lyapunov function for asynchronous control of discrete-time switched systems. (January 2022)

• Record Type: Journal Article
• Authors: Cui, Jiahao; Wang, Ruihua; Fei, Shumin
• Other Names: Yang Yongsheng guest-editor.
• Is Part Of: Transactions of the Institute of Measurement and Control. Volume 44:Number 1(2022)
• Page Start: 162
• Page End: 171
• Publication Date: 2022-01
• Subjects: Switched systems -- asynchronous control -- globally uniformly exponentially stability -- multiple convex Lyapunov function -- mode-dependent integrated dwell time; Automatic control -- Periodicals; Measuring instruments -- Periodicals; Commande automatique -- Périodiques; Mesure -- Instruments -- Périodiques; 681.2
• DOI: 10.1177/01423312211026547
• Languages: English
• ISSNs: 0142-3312

Abstract

In this paper, the problem of asynchronous control for a class of discrete-time switched systems is investigated under mode-dependent integrated dwell time (MDIDT) switching. By constructing a time-dependent convex function, a multiple convex Lyapunov function (MCLF) is firstly proposed for the asynchronous control of the switched systems. Under the MDIDT switching strategy, the matching interval is divided reasonably, and the convex function combination is constructed on the partitioned interval. Under asynchronous switching, the Lyapunov function is continuous when the subsystem mode is switched, but discrete when the controller mode is changed. Then, the increase of the Lyapunov function in the mismatched interval will be offset by the attenuation in the matched interval. In light of these merits, the stability results of the system are deduced, and the asynchronous controller is devised to guarantee the globally uniformly exponentially stability of the closed-loop system. Comparing with the traditional asynchronous control methods, the proposed method has less conservative results and larger stability regions. Finally, a numerical example and an application example are demonstrated to verify the validity and superiority of the asynchronous control scheme.