An improved stability criterion for linear time-varying delay systems

• Main Authors: Wenxi Feng, Fei Luo, Wenyong Duan, Yan Li, Jian Chen
• Format: Article
• Language: English
• Published: Taylor & Francis Group 2020-04-01
• Series: Automatika
• Subjects: delay-dependent stability; lyapunov–krasovskii functional; linear matrix inequalities; time-delayed system; time-varying delay
• Online Access: http://dx.doi.org/10.1080/00051144.2019.1706885

This paper considers the stability problem of linear systems with time-varying delays. A modified Lyapunov–Krasovskii functional (LKF) is constructed, which consists of delay-dependent matrices and double integral items under two time-varying subintervals. Based on the modified LKF, a less conservative stability criterion than some previous ones is derived. Furthermore, to obtain a tighter bound of the integral terms, the quadratic generalized free-weighting matrix inequality (QGFMI) is fully applied to different delay subintervals, which further reduces the conservatism of the stability criterion. Finally, three numerical examples are presented to show the effectiveness of the proposed approach.