New Finite-Time Stability Criterion for Piecewise Linear Systems through a Finsler's Lemma Approach

This note deals with the Stability in Finite Time (FTS) of a special class of hybrid dynamic system (HDS) which are the Piecewise Linear (PWL) systems. New condition for FTS of this type of systems has been investigated. The new conditions proposed in this notice are on the one hand the result of the Finsler's lemma and on the other hand a combination between this lemma and the S-procedure. These conditions are given in terms of Linear Matrix Inequalities (LMI). A Numerical example is stated to illustrate the proposed approaches and to compare its effectiveness with the previous results, based on an S-procedure approach.