Notes on Stability of Time-Delay Systems: Bounding Inequalities and Augmented Lyapunov-Krasovskii Functionals



Zhang, Chuan-Ke, He, Yong, Jiang, Lin ORCID: 0000-0001-6531-2791 and Wu, Min
(2017) Notes on Stability of Time-Delay Systems: Bounding Inequalities and Augmented Lyapunov-Krasovskii Functionals. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 62 (10). pp. 5331-5336.

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Abstract

The bounding inequalities and the Lyapunov-Krasovskii functionals (LKFs) are important for the stability analysis of time-delay systems. Much attention has been paid to develop tighter inequalities for improving stability criteria, while the contribution of the LKFs has not been considered when discussing the relationship between the tightness of inequalities and the conservatism of criteria. This note is concerned with this issue. Firstly, it is proved that, when a simple LKF is applied, the stability criteria obtained by the Wirtinger-based inequality and the Jensen inequality are equivalent although the Wirtinger-based inequality is tighter. It means that the tighter inequality does not always lead to a less conservative criterion. Secondly, it is found that a suitable augmented LKF with necessary integral vectors in its derivative is required to achieve the advantage of the Wirtinger-based inequality. Based on this observation, two delay-product-type terms are introduced into the LKF to establish new stability criteria. Finally, a numerical example is given to verify the equivalence statements and to show the benefit of the proposed criteria.

Item Type: Article
Uncontrolled Keywords: Augmented Lyapunov-Krasovskii functional, bounding inequalities, stability, time-delay system
Depositing User: Symplectic Admin
Date Deposited: 25 Oct 2017 14:10
Last Modified: 15 Mar 2024 04:55
DOI: 10.1109/TAC.2016.2635381
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3010683