A novel integral inequality and its application to stability analysis of linear system with multiple time delays

Jin, Li, He, Yong and Jiang, Lin ORCID: 0000-0001-6531-2791 (2022) A novel integral inequality and its application to stability analysis of linear system with multiple time delays Applied Mathematics Letters, 124. p. 107648. ISSN 0893-9659, 1873-5452

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Abstract

The integral inequality plays a key role in developing delay-dependent stability criteria for the linear system with multiple time delays. This paper investigates a novel integral inequality to bound the integral terms in the derivative of the Lyapunov–Krasovskii functional (LKF). Compared with the auxiliary function-based integral inequality, the presented integral inequality is more general. By removing the involved auxiliary function, the integral term in the bound is linearly represented with a sequence of integrals only related to the system state. After a newly augmented LKF is constructed with multiple integral terms concerning the relationships among multiple delays, an adjustable and relaxed stability criterion is established in terms of linear matrix inequalities using the proposed inequality. Two numerical examples are given to show the merits of the proposed method.

Item Type:	Article
Uncontrolled Keywords:	Stability analysis, Multiple time delays, Multiple integral terms, Integral inequality, Linear matrix inequalities
Divisions:	Faculty of Science & Engineering > School of Electrical Engineering, Electronics and Computer Science
Depositing User:	Symplectic Admin
Date Deposited:	14 Sep 2021 10:01
Last Modified:	01 Mar 2026 00:02
DOI:	10.1016/j.aml.2021.107648
Related Websites:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3137051
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