Stability analysis of switched systems with all subsystems unstable: A matrix polynomial approach

New stability results for discrete-time switched systems under admissible edge-dependent average persistent dwell-time or admissible edge-dependent persistent dwell-time switching

This paper is devoted to the stability analysis of a class of discrete-time switched systems under newly designed switching regularities. The utilized switching is extended from the primitive mode-dependent persistent dwell-time switching. By integrating the existing admissible edge-dependent average dwell-time switching into the mode-dependent persistent dwell-time regime, a novel admissible edge-dependent average persistent dwell-time strategy involving the notion of admissible transition edges is proposed. The integrated admissible edge-dependent average dwell-time switching has been confirmed to be superior to mode-dependent average dwell-time switching. This superiority makes the proposed switching more general than the relaxed mode-dependent persistent dwell-time switching in the literature. Even if the embedded admissible edge-dependent average dwell-time restrictions degrade to admissible edge-dependent dwell-time ones under special parameter settings, the resulting admissible edge-dependent persistent dwell-time switching retains the advantage of admissible transition edges to generalize the original mode-dependent persistent dwell-time switching. Meanwhile, to remove the switching information reliance in the existing multiple convex Lyapunov functions, an improved multiple convex Lyapunov function method is devised. The designed Lyapunov function can be used to implement broader feasible ranges and tighter lower bounds of admissible edge-dependent average persistent dwell-time (or admissible edge-dependent persistent dwell-time). Finally, the validity and efficiency of the presented approaches are illustrated by a three-phase inverter and a numerical example.

Passivity-based event-triggered control for a class of switched nonlinear systems

A static output feedback based event-triggered control mechanism for a class of switched nonlinear systems with a passivity property is proposed in this paper. Each subsystem of such a switched system does not necessarily have passivity in the classical sense, while maintaining the passivity property only on the active time intervals. Moreover, passivity is based on multiple storage functions and the storage functions are allowed to increase at switching instants. The proposed event-triggered output feedback controller can not only maintain asymptotic stability but also exclude Zeno behavior under some conditions. Finally, a numerical example is presented to illustrate the effectiveness of the method.