Nonlinear perturbation of a class of conservative linear system

Shantanu Singh*, George Weiss

*Corresponding author for this work

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

1 Scopus citations

Abstract

In this article we show the existence and uniqueness of classical and generalized solutions of a class of nonlinear infinite dimensional systems. Such systems are obtained by modifying the second order differential equation that is part of the description of conservative linear systems "out of thin air"introduced by M. Tucsnak and G. Weiss in 2003. The modified system contains a new nonlinear damping term, that is maximal monotone and possibly set-valued and hence state trajectories obey a differential inclusion. We show that this new class of nonlinear infinite dimensional systems is incrementally scattering passive (hence well-posed). The proof is based on the Crandall-Pazy theorem which shows that the Lax-Phillips type nonlinear semigroup (that represents the entire system) is a contraction.

Original languageEnglish
Title of host publication2022 IEEE 61st Conference on Decision and Control, CDC 2022
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages396-402
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

Funding

FundersFunder number
Horizon 2020 Framework Programme
Horizon 2020765579

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