Finite-time stability of a class of continuous-time non-homogeneous switched systems

Abstract

This paper is concerned with the finite-time stability problem of a class of linear continuous-time non-homogeneous switched systems under a time-dependent switching signal constrained by a dwell-time T. Once the finite-time stability is guaranteed, one of the main results of the paper guarantees that any system trajectory starting in a subset Ω1 of the state-space will remain in Ω2⊃Ω1 over a finite time interval and for any switching sequence with a dwell-time T̄≥T. The finite-time stability conditions are provided in the form of bilinear matrix inequalities (BMIs), which can be transformed to linear matrix inequalities (LMIs) by means of a step-by-step procedure that includes the computation of the sets Ω1 and Ω2 by the knowledge of the system operating range. Three illustrative examples are used to show the validity of the results.