Feedback Stabilization of a Class of Diagonal Infinite-Dimensional Systems With Delay Boundary Control

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Title: Feedback Stabilization of a Class of Diagonal Infinite-Dimensional Systems With Delay Boundary Control
Authors: Lhachemi, HugoPrieur, Christophe
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Date: Jan-2021
Online since: 2021-02-23T16:42:24Z
Abstract: This article studies the boundary feedback stabilization of a class of diagonal infinite-dimensional boundary control systems. In the studied setting, the boundary control input is subject to a constant delay while the open-loop system might exhibit a finite number of unstable modes. The proposed control design strategy consists of two main steps. First, a finite-dimensional subsystem is obtained by truncation of the original infinitedimensional system (IDS) via modal decomposition. It includes the unstable components of the IDS and allows the design of a finite-dimensional delay controller by means of the Artstein transformation and the pole-shifting theorem. Second, it is shown via the selection of an adequate Lyapunov function that: 1) the finite-dimensional delay controller successfully stabilizes the original IDS and 2) the closed-loop system is exponentially input-to-state stable (ISS) with respect to distributed disturbances. Finally, the obtained ISS property is used to derive a small gain condition ensuring the stability of an IDS-ODE interconnection.
Funding Details: European Commission - European Regional Development Fund
Science Foundation Ireland
Funding Details: I-Form Industry Partners
Type of material: Journal Article
Publisher: IEEE Transactions on Automatic Control
Journal: IEEE Transactions on Automatic Control
Volume: 66
Issue: 1
Start page: 105
End page: 120
Copyright (published version): 2021 IEEE
Keywords: Distributed parameter systemsDelay boundary controlLyapunov functionPartial differential equation (PDE)-ordinary differential equation (ODE) interconnection
DOI: 10.1109/TAC.2020.2975003
Language: en
Status of Item: Peer reviewed
This item is made available under a Creative Commons License:
Appears in Collections:Electrical and Electronic Engineering Research Collection
I-Form Research Collection

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