On the derivation of stability properties for time-delay systems without constraint on the time-derivative of the initial condition
File(s)
Accepted version
Author(s)
Lhachemi, Hugo
Shorten, Robert
Type
Journal Article
Abstract
Stability of retarded differential equations is closely related to the existence of Lyapunov–Krasovskii functionals. Even if a number of converse results have been reported regarding the existence of such functionals, there is a lack of constructive methods for their selection. For certain classes of time-delay systems for which such constructive methods are lacking, it was shown that Lyapunov–Krasovskii functionals that are also allowed to depend on the time-derivative of the state-trajectory are efficient tools for the study of the stability properties. However, in such an approach, the initial condition needs to be assumed absolutely continuous with a square integrable weak derivative. In addition, the stability results hold for initial conditions that are evaluated based on the magnitude of both the initial condition and its time-derivative. The main objective of this article is to show that, for certain classes of time-delay systems, the aforementioned stability results can actually be extended to initial conditions that are only assumed continuous and that are evaluated in uniform norm.
Date Issued
2021-11
Date Acceptance
2020-12-10
Citation
IEEE Transactions on Automatic Control, 2021, 66 (11), pp.5401-5406
ISSN
0018-9286
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Start Page
5401
End Page
5406
Journal / Book Title
IEEE Transactions on Automatic Control
Volume
66
Issue
11
Copyright Statement
© 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Identifier
https://ieeexplore.ieee.org/document/9308952
Subjects
math.OC
math.OC
Industrial Engineering & Automation
0102 Applied Mathematics
0906 Electrical and Electronic Engineering
0913 Mechanical Engineering
Publication Status
Published
Date Publish Online
2020-12-25