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. ISSN 0096-3003, 1873-5649

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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:	22 May 2026 22:16
DOI:	10.1016/j.amc.2019.04.004
Related Websites:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3043351
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