Finite-time boundedness and weighted L2-gain analysis for uncertain switched linear systems with both stable and unstable time-delay subsystems

This paper studies the finite-time boundedness (FTB) and finite-time weighted L₂-gain problems for switched systems consisting of both stable and unstable subsystems, the polytopic uncertainties and time-varying delays are also taken into account. A new switching law and a novel binary-switching Lyapunov-Krasovskii functional are invoked at the first attempt to sufficiently exploit the different properties of stable and unstable subsystems. The FTB criteria and a class of less conservative switching signals with average dwell time are firstly derived for the switched linear systems with time-varying delays, upon which, the investigations of finite-time weighted L₂-gain performance are then performed. A numerical example is given to illustrate the validity and the advantage of the developed findings.