Lyapunov characterizations on input-to-state stability of nonlinear systems with infinite delays

Xiang Xu; Lu Liu; Gang Feng

doi:10.1016/j.automatica.2022.110585

Lyapunov characterizations on input-to-state stability of nonlinear systems with infinite delays

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

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Author(s)

Related Research Unit(s)

Department of Biomedical Engineering

Detail(s)

Original language	English
Article number	110585
Journal / Publication	Automatica
Volume	146
Online published	11 Sept 2022
Publication status	Published - Dec 2022

Link(s)

DOI	DOI https://doi.org/10.1016/j.automatica.2022.110585 Final Published version
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Attachment(s)	Documents 117767726.pdf Post-print, 348 KB, PDF Publisher's Copyright Statement COPYRIGHT TERMS OF DEPOSITED POSTPRINT FILE: © 2022. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/.
Link to Scopus	https://www.scopus.com/record/display.uri?eid=2-s2.0-85137641412&origin=recordpage
Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(296061ba-3320-4880-972f-564fd962ad02).html

Abstract

This paper addresses Lyapunov characterizations on input-to-state stability (ISS) of time-varying nonlinear systems with infinite delays. With novel ISS definitions in the case of nonlinear systems with infinite delays, we present several results on their ISS Lyapunov characterizations in the form of both ISS Lyapunov theorems and converse ISS Lyapunov theorems. It is shown that an infinite-delayed system is (locally) ISS if it has a (local) ISS Lyapunov functional, and conversely, there exists a (local) ISS Lyapunov functional if it is (locally) ISS. To prove the converse ISS Lyapunov theorems, we establish a key technical lemma bridging ISS/LISS and robust asymptotic stability of systems with infinite delays and two converse Lyapunov theorems concerning robust asymptotic stability of systems with infinite delays. Two distinctive advantages of this work are that a large class of infinite dimensional spaces are allowed and the results are established based on a more general Lipschitz condition, i.e., the right hand side Lipschitz (RS-L) condition. An example is provided for illustration of the obtained results.