Stability analysis of linear systems with time-varying delay via a quadratic function negative-definiteness determination method



Long, Fei, Lin, Wen-Juan, He, Yong, Jiang, Lin ORCID: 0000-0001-6531-2791 and Wu, Min
(2020) Stability analysis of linear systems with time-varying delay via a quadratic function negative-definiteness determination method. IET CONTROL THEORY AND APPLICATIONS, 14 (11). pp. 1478-1485.

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Abstract

This study aims to carry out the stability analysis of linear systems with a time-varying delay. It is known that the negative-definite condition of the derivative of a Lyapunov-Krasovskii functional (LKF) can be determined using the convex combination method if the convexity requirement is satisfied by the derivative of the LKF. However, this method is not feasible in cases where the LKF's derivative is a quadratic function. To address this problem, this study proposes a novel negativedefiniteness determination lemma that encompasses the previous lemmas as its special cases and shows less conservatism. Then, this lemma is employed to derive a stability criterion, and its superiority is demonstrated using three examples.

Item Type: Article
Uncontrolled Keywords: stability, Lyapunov methods, time-varying systems, asymptotic stability, linear systems, linear matrix inequalities, delays, stability analysis, linear systems, time-varying delay, quadratic function negative-definiteness determination method, negative-definite condition, Lyapunov-Krasovskii functional, convex combination method, convexity requirement, LKF's derivative, novel negative-definiteness determination lemma, stability criterion
Depositing User: Symplectic Admin
Date Deposited: 24 Aug 2020 07:34
Last Modified: 18 Jan 2023 23:36
DOI: 10.1049/iet-cta.2019.0471
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3098464