Semi-time-dependent stabilization results for asynchronously switched systems: An extended persistent dwell time switching strategy involving admissible transition information

Abstract

This study investigates the stabilization problem for a kind of continuous-time asynchronously switched systems via a set of edge- or mode-dependent state-feedback controllers. To this end, an innovative switching strategy of admissible chain-dependent (or admissible edge-dependent) persistent dwell time property is presented by injecting the admissible transition chain (or admissible transition edge) notion into the existing persistent dwell time concept. Based on the admissible transition edges in a directed graph reported in the literature, the corresponding admissible transition chains can be determined. The individual allocation of transition weights for each admissible transition chain makes the presented admissible chain-dependent persistent dwell time switching less conservative than the other presented admissible edge-dependent persistent dwell time and the already existing mode-dependent persistent dwell time switching. Further, different from the Lyapunov functions commonly used in previous asynchronous stabilization works, a new semi-time-dependent Lyapunov function in a unique form that fits the nature of the discussed systems is suggested to provide a broader family of allowable switching signals. By the introduced switching and Lyapunov function approaches, new stability and stabilization criteria are formulated, through which the expected edge- or mode-dependent state-feedback controllers are devised. At last, the validity and applicability of the obtained stabilization solutions are demonstrated by a numerical example and a practical thermal system.