New results on stability analysis of systems with time-varying delays using a generalized free-matrix-based inequality

This paper addresses the delay-dependent stability problem of linear systems with interval time-varying delays. A generalized free-matrix-based inequality is proposed and employed to derive stability conditions, which are less conservative than the Bessel-Legendre inequality. An augmented Lyapunov-Krasovskii functional is tailored for the generalized free-matrix-based inequality. Then, some items in the Lyapunov-Krasovskii functionals are integrated so as to relax its positive definite condition, which provides a more accurate lower bound for the Lyapunov-Krasovskii functionals. Therefore, some less conservative stability criteria are presented. Two numerical examples illustrate the effectiveness of the method. (C) 2019 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.