Finite-Time Stability Analysis for Piecewise Linear Systems

This paper deals with the Finite-time stability (FTS) analysis for PieceWise Linear (PWL) systems. Indeed, this issue is relevant since it is highly difficult to study the stability in the sense of Lyapunov for this class of systems. Moreover, this issue was hardly adressed in the literature. The analysis is achieved through a Lyapunov-like approach and provides a sufficient condition for the FTS of PWL system. The S-procedure was used in order to limit its conservativeness. This condition is given in terms of Linear Matrix Inequalities (LMI) that are easily tractable. A numerical example is presented to illustrate the advantages of the proposed methodology.