A time-delay approach to Lie-brackets-based averaging of affine systems

Jin Zhang*, Emilia Fridman

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

In this paper, we study stability of affine systems with a small parameter ϵ > 0. We present a time-delay approach to Lie-brackets-based averaging, where we transform the system to a time-delay one. The latter has a form of perturbed Lie-brackets system. The practical stability of the time-delay system guarantees the same for the original system. We present the direct Lyapunov-Krasovskii method for the time-delay system and provide sufficient conditions for the local input-to-state stability of the original one. We further apply the results to stabilization under unknown control directions. In contrast to the existing results that are all qualitative, we derive constructive linear matrix inequalities for finding quantitative upper bounds on ϵ that ensures the practical stability and on the resulting ultimate bound. We also give new qualitative conditions for semiglobal stabilization. Numerical examples illustrate the efficiency of the results.

Original languageEnglish
Title of host publication2022 IEEE 61st Conference on Decision and Control, CDC 2022
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages6895-6901
Number of pages7
ISBN (Electronic)9781665467612
DOIs
StatePublished - 2022
Event61st IEEE Conference on Decision and Control, CDC 2022 - Cancun, Mexico
Duration: 6 Dec 20229 Dec 2022

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2022-December
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370

Conference

Conference61st IEEE Conference on Decision and Control, CDC 2022
Country/TerritoryMexico
CityCancun
Period6/12/229/12/22

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