On the derivation of stability properties for time-delay systems without constraint on the time-derivative of the initial condition

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Title: On the derivation of stability properties for time-delay systems without constraint on the time-derivative of the initial condition
Authors: Lhachemi, HugoShorten, Robert
Permanent link: http://hdl.handle.net/10197/12733
Date: Nov-2021
Online since: 2022-01-14T16:23:18Z
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 paper 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.
Funding Details: European Commission - European Regional Development Fund
Science Foundation Ireland
Type of material: Journal Article
Publisher: IEEE
Journal: IEEE Transactions on Automatic Control
Volume: 66
Issue: 11
Start page: 5401
End page: 5406
Copyright (published version): 2020 IEEE
Keywords: Time-delay systemsRetarded differential equationsLyapunov-Krasovskii functionalsStability propertiesRegularity of the initial condition
DOI: 10.1109/TAC.2020.3047358
Language: en
Status of Item: Peer reviewed
This item is made available under a Creative Commons License: https://creativecommons.org/licenses/by-nc-nd/3.0/ie/
Appears in Collections:Electrical and Electronic Engineering Research Collection
I-Form Research Collection

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