ISS of Rapidly Time-Varying Systems Via a Novel Presentation and Delay-Free Transformation

Rami Katz, Emilia Fridman, Frédéric Mazenc

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

Abstract

We treat input-to-state stability (ISS) of linear continuous-time systems with multiple time-scales. These systems contain rapidly-varying, piecewise continuous and almost periodic coefficients with small parameters (time-scales). Our method relies on a novel delay-free system transformation in conjunction with a new system presentation, where the rapidly-varying coefficients are scalars that have zero average. We employ time-varying Lyapunov functions for ISS analysis. The analysis yields LMI conditions for ISS, leading to explicit bounds on the small parameters, decay rate and ISS gains. The novel system presentation plays a crucial role in the ISS analysis by allowing for essentially less conservative upper bounds on terms containing the small parameters. The derived LMIs are accompanied by suitable feasibility guarantees. Numerical examples demonstrate the efficacy of the proposed approach in comparison to existing methods.

Original languageEnglish
Title of host publication2023 62nd IEEE Conference on Decision and Control, CDC 2023
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages8763-8768
Number of pages6
ISBN (Electronic)9798350301243
DOIs
StatePublished - 2023
Event62nd IEEE Conference on Decision and Control, CDC 2023 - Singapore, Singapore
Duration: 13 Dec 202315 Dec 2023

Publication series

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

Conference

Conference62nd IEEE Conference on Decision and Control, CDC 2023
Country/TerritorySingapore
CitySingapore
Period13/12/2315/12/23

Keywords

  • averaging
  • ISS
  • Lyapunov methods
  • stability
  • time-varying systems

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