Output-based optimal L1-gain control of weighted edge-dependent switching positive systems by a new copositive Lyapunov function. (November 2022)

• Record Type: Journal Article
• Authors: Hu, Shuoyang; Wang, Ruihua; Jiao, Ticao; Fei, Shumin
• Is Part Of: Nonlinear analysis. Volume 46(2022)
• Publication Date: 2022-11
• Subjects: Switched positive linear systems -- Weighted edge-dependent average dwell time -- Multiple convex copositive Lyapunov function -- L1-gain control; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2022.101260
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: In this paper, the weighted L 1 -gain analysis and control synthesis for switched positive linear systems are investigated via a weighted edge-dependent average dwell time approach. First, a novel multiple convex copositive Lyapunov function is devised in a polytopic form with clock-dependent function coefficients, which not merely upgrades the degrees of freedom of the Lyapunov function considerably, but also permits the descent at switching instants. By weighted edge-dependent switching technique, the feasible switching zone is greatly extended, and the dwell time constraint is eliminated for each subsystem. In a particular scenario, the lower bound on the weighted sum of all dwell times can be even erased thoroughly, and the relevant non-weighted L 1 -gain results can be derived. Furthermore, two L 1 -gain convex control laws are derived in time-varying forms, comprising state feedback and output feedback, which can be updated continuously during the running time of systems. Finally, a positive circuit system and two numerical examples are presented to conduct comparative studies with other clock-dependent Lyapunov function results, suggesting that the proposed results perform better under low complexity on L 1 -gain, switching zone, computation time, etc, and improve transient performances such as settling time and overshoot.