Robustness of constant-delay predictor feedback for in-domain stabilization of reaction–diffusion PDEs with time- and spatially-varying input delays

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Title: Robustness of constant-delay predictor feedback for in-domain stabilization of reaction–diffusion PDEs with time- and spatially-varying input delays
Authors: Lhachemi, HugoPrieur, ChristopheShorten, Robert
Permanent link: http://hdl.handle.net/10197/11968
Date: Jan-2021
Online since: 2021-02-23T16:57:22Z
Abstract: This paper discusses the in-domain feedback stabilization of reaction–diffusion PDEs with Robin boundary conditions in the presence of an uncertain time- and spatially-varying delay in the distributed actuation. The proposed control design strategy consists of a constant-delay predictor feedback designed based on the known nominal value of the control input delay and is synthesized on a finite-dimensional truncated model capturing the unstable modes of the original infinite-dimensional system. By using a small-gain argument, we show that the resulting closed-loop system is exponentially stable provided that the variations of the delay around its nominal value are small enough. The proposed proof actually applies to any distributed-parameter system associated with an unbounded operator that 1) generates a -semigroup on a weighted space of square integrable functions over a compact interval; and 2) is self-adjoint with compact resolvent.
Funding Details: European Commission - European Regional Development Fund
Science Foundation Ireland
Funding Details: I-Form industry partners
Type of material: Journal Article
Publisher: Elsevier
Journal: Automatica
Volume: 123
Copyright (published version): 2020 Elsevier
Keywords: Delayed distributed actuationSpatially-varying delayDistributed parameter systemsPredictor feedbackReaction-diffusion equation
DOI: 10.1016/j.automatica.2020.109347
Language: en
Status of Item: Peer reviewed
This item is made available under a Creative Commons License: https://creativecommons.org/licenses/by-nc-nd/3.0/ie/
Appears in Collections:Electrical and Electronic Engineering Research Collection
I-Form Research Collection

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