Integral input-to-state stability of switched delay systems composed of unstable subsystems

Abstract

This paper is concerned with the problem of integral input-to-state stability (iISS) for a class of continuous-time switched systems with time-varying delays, whose subsystems can be all unstable. By constructing a discretized multiple Lyapunov functional, the iISS for switched delay systems in nonlinear context is firstly established. Then, a special class of linear systems-bilinear switched delay systems, which can only achieve iISS instead of ISS (input-to-state stability) is considered. By resorting to polytope extremum theory, the system equation is transformed into a polytope equation. Subsequently, by using a linear interpolation formula method, sufficient computable conditions for iISS with dwell time switching are presented. A numerical example is provided to illustrate the effectiveness of our approach.