A Sufficient Condition on Polynomial Inequalities and its Application to Interval Time-Varying Delay Systems

Liu, Meng, He, Yong and Jiang, Lin ORCID: 0000-0001-6531-2791 (2023) A Sufficient Condition on Polynomial Inequalities and its Application to Interval Time-Varying Delay Systems Journal of Advanced Computational Intelligence and Intelligent Informatics, 27 (4). pp. 683-690. ISSN 1343-0130, 1883-8014

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Abstract

This article examines the stability problem of systems with interval time-varying delays. In the derivation of Lyapunov–Krasovskii functional (LKF), non-convex higher-degree polynomials may arise with respect to interval time-varying delays, making it difficult to determine the negative definiteness of LKF’s derivative. This study was conducted to obtain stability conditions that can be described as linear matrix inequalities (LMIs). By considering the idea of matrix transition and introducing the delay-dependent augmented vector, a novel higher-degree polynomial inequality is proposed under the condition that the lower bound of the polynomial function variable is non-zero, which encompasses the existing lemmas as its special cases. Then, benefiting from this inequality, a stability criterion is derived in terms of LMIs. Finally, several typical examples are presented to verify the availability and strength of the stability condition.

Item Type:	Article
Uncontrolled Keywords:	stability, time-varying delay, polynomial in-equality, negative-definiteness condition
Divisions:	Faculty of Science & Engineering > School of Electrical Engineering, Electronics and Computer Science
Depositing User:	Symplectic Admin
Date Deposited:	10 Aug 2023 10:23
Last Modified:	01 Mar 2026 03:13
DOI:	10.20965/jaciii.2023.p0683
Open Access URL:	https://www.fujipress.jp/jaciii/jc/jacii0027000406...
Related Websites:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3172171
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