Output-based optimal [formula omitted]-gain control of weighted edge-dependent switching positive systems by a new copositive Lyapunov function

Abstract

In this paper, the weighted L1-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 L1-gain results can be derived. Furthermore, two L1-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 L1-gain, switching zone, computation time, etc, and improve transient performances such as settling time and overshoot.