Improved observer design for heat equation with constant measurement delay via Legendre polynomials

Jin Zhang, Wen Kang, Emilia Fridman, Alexandre Seuret

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

1 Scopus citations

Abstract

In this paper, we present improved results on observer design for 1D heat equation. We first introduce an observer under delayed spatially point measurements that leads to an estimation error with time-delay. Inspired by recent developments in the area of delayed ODEs, we suggest augmented Lyapunov functionals based on the Legendre polynomials. Then, sufficient exponential stability conditions are derived in the form of linear matrix inequalities (LMIs) that are parameterized by the degree of the polynomials. Finally, a numerical example illustrates the efficiency of the results that allow to enlarge the value of delay preserving the stability by more than 20%.

Original languageEnglish
Title of host publication2020 59th IEEE Conference on Decision and Control, CDC 2020
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4448-4453
Number of pages6
ISBN (Electronic)9781728174471
DOIs
StatePublished - 14 Dec 2020
Event59th IEEE Conference on Decision and Control, CDC 2020 - Virtual, Jeju Island, Korea, Republic of
Duration: 14 Dec 202018 Dec 2020

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2020-December
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370

Conference

Conference59th IEEE Conference on Decision and Control, CDC 2020
Country/TerritoryKorea, Republic of
CityVirtual, Jeju Island
Period14/12/2018/12/20

Funding

FundersFunder number
Israel Science Foundation673/19, 1128/14
Centre National de la Recherche Scientifique
Council for Higher Education
Ministry of Science and Technology, Israel

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