Finite-time stability and boundedness for linear switched singular positive time-delay systems with finite-time unstable subsystems

Abstract

In this paper, the problem of finite-time stability and finite-time boundedness for a class of linear switched singular positive time-delay systems with finite-time unstable subsystems is investigated. Necessary and sufficient positivity conditions for the systems are firstly presented by using the state-space singular value decomposition and monomial coordinate transformation methods. A class of quasi-alternative switching signals is then designed to analyze the switching behaviours of the systems. Mode-dependent average dwell time (MDADT) switching, consisting of a slow mode-dependent average dwell time (SMDADT) switching and a fast mode-dependent average dwell time (FMDADT) switching, is applied to the systems whose subsystems are stable and unstable. By establishing a suitable copositive Lyapunov-Krasovskii functional and adopting the MDADT switching strategy, all sufficient conditions guaranteeing the finite-time stability and finite-time boundedness of the considered systems are formulated in terms of linear vector inequalities as well as linear matrix inequalities. Several numerical examples are provided to illustrate the effectiveness of the proposed methods. Notably, a positive electrical circuit model is utilized to demonstrate the applicability of the theoretical results.