Stability analysis of systems with time-varying delay via novel augmented Lyapunov-Krasovskii functionals and an improved integral inequality



Long, Fei, Jiang, Lin ORCID: 0000-0001-6531-2791, He, Yong and Wu, Min
(2019) Stability analysis of systems with time-varying delay via novel augmented Lyapunov-Krasovskii functionals and an improved integral inequality. APPLIED MATHEMATICS AND COMPUTATION, 357. pp. 325-337.

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Abstract

Delay-dependent stability analysis of linear systems with a time-varying delay is investigated in this paper. Firstly, instead of developing a Lyapunov–Krasovskii functional (LKF) including augmented non-integral quadratic terms as usual, this paper proposes two augmented-integral-function based LKFs, which can reflect closer relationships among system states. Secondly, to bound the derivative of LKF more accurately, a new integral inequality with several free matrices is developed. Compared with the free-matrix-based integral inequality, this inequality can provide additional freedom due to the free matrices introduced. Then, by employing those LKFs and the improved integral inequality, several delay-dependent stability criteria are established for two types of delays. Finally, two numerical examples are given to demonstrate the superiority of the proposed method.

Item Type: Article
Uncontrolled Keywords: Time-delay system, Time-varying delay, Stability, Augmented Lyapunov-Krasovskii functional
Depositing User: Symplectic Admin
Date Deposited: 30 May 2019 09:32
Last Modified: 19 Jan 2023 00:42
DOI: 10.1016/j.amc.2019.04.004
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3043351