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JACIII Vol.27 No.4 pp. 683-690
doi: 10.20965/jaciii.2023.p0683
(2023)

Research Paper:

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

Meng Liu*1,*2,*3 ORCID Icon, Yong He*1,*2,*3,† ORCID Icon, and Lin Jiang*4 ORCID Icon

*1School of Automation, China University of Geosciences
388 Lumo Road, Hongshan District, Wuhan, Hubei 430074, China

*2Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems
388 Lumo Road, Hongshan District, Wuhan, Hubei 430074, China

*3Engineering Research Center of Intelligent Technology for Geo-Exploration, Ministry of Education
388 Lumo Road, Hongshan District, Wuhan, Hubei 430074, China

*4Department of Electrical Engineering and Electronics, University of Liverpool
Brownlow Hill, Liverpool, Merseyside L 3, United Kingdom

†Corresponding author

Received:
November 23, 2022
Accepted:
April 11, 2023
Published:
July 20, 2023
Creative Commons License
Keywords:
stability, time-varying delay, polynomial inequality, negative-definiteness condition
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.

Cite this article as:
M. Liu, Y. He, and L. Jiang, “A Sufficient Condition on Polynomial Inequalities and its Application to Interval Time-Varying Delay Systems,” J. Adv. Comput. Intell. Intell. Inform., Vol.27 No.4, pp. 683-690, 2023.
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Last updated on Apr. 22, 2024