Observer Design for a Class of Parabolic Systems with Large Delays and Sampled Measurements

Tarek Ahmed-Ali; Emilia Fridman; Fouad Giri; Mohamed Kahelras; Francoise Lamnabhi-Lagarrigue; Laurent Burlion

doi:https://doi.org/10.1109/TAC.2019.2941434

Observer Design for a Class of Parabolic Systems with Large Delays and Sampled Measurements

Tarek Ahmed-Ali, Emilia Fridman, Fouad Giri, Mohamed Kahelras, Francoise Lamnabhi-Lagarrigue, Laurent Burlion

School of Engineering, Mechanical & Aerospace Engineering

Rutgers, The State University

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

In this paper, we design a novel observer for a class of semilinear heat one dimmensional (1-D) equations under the delayed and sampled point measurements. The main novelty is that the delay is arbitrary. To handle any arbitrary delay, the observer is constituted of a chain of subobservers. Each subobserver handles a fraction of the considered delay. The resulting estimation error system is shown to be exponentially stable under a sufficient number of subobservers is used. The stability analysis is based on a specific Lyapunov-Krasovskii functional and the stability conditions are expressed in terms of linear matrix inequalities (LMIs).

Original language	American English
Article number	8836621
Pages (from-to)	2200-2206
Number of pages	7
Journal	IEEE Transactions on Automatic Control
Volume	65
Issue number	5
DOIs	https://doi.org/10.1109/TAC.2019.2941434
State	Published - May 2020

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

Keywords

Chain observers
delayed output
parabolic systems

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https://doi.org/10.1109/TAC.2019.2941434

Cite this

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abstract = "In this paper, we design a novel observer for a class of semilinear heat one dimmensional (1-D) equations under the delayed and sampled point measurements. The main novelty is that the delay is arbitrary. To handle any arbitrary delay, the observer is constituted of a chain of subobservers. Each subobserver handles a fraction of the considered delay. The resulting estimation error system is shown to be exponentially stable under a sufficient number of subobservers is used. The stability analysis is based on a specific Lyapunov-Krasovskii functional and the stability conditions are expressed in terms of linear matrix inequalities (LMIs).",

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AU - Ahmed-Ali, Tarek

AU - Fridman, Emilia

AU - Giri, Fouad

AU - Kahelras, Mohamed

AU - Lamnabhi-Lagarrigue, Francoise

AU - Burlion, Laurent

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N2 - In this paper, we design a novel observer for a class of semilinear heat one dimmensional (1-D) equations under the delayed and sampled point measurements. The main novelty is that the delay is arbitrary. To handle any arbitrary delay, the observer is constituted of a chain of subobservers. Each subobserver handles a fraction of the considered delay. The resulting estimation error system is shown to be exponentially stable under a sufficient number of subobservers is used. The stability analysis is based on a specific Lyapunov-Krasovskii functional and the stability conditions are expressed in terms of linear matrix inequalities (LMIs).

AB - In this paper, we design a novel observer for a class of semilinear heat one dimmensional (1-D) equations under the delayed and sampled point measurements. The main novelty is that the delay is arbitrary. To handle any arbitrary delay, the observer is constituted of a chain of subobservers. Each subobserver handles a fraction of the considered delay. The resulting estimation error system is shown to be exponentially stable under a sufficient number of subobservers is used. The stability analysis is based on a specific Lyapunov-Krasovskii functional and the stability conditions are expressed in terms of linear matrix inequalities (LMIs).

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Observer Design for a Class of Parabolic Systems with Large Delays and Sampled Measurements

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