ISS Property with respect to boundary disturbances for a class of Riesz-spectral boundary control systems

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Title: ISS Property with respect to boundary disturbances for a class of Riesz-spectral boundary control systems
Authors: Lhachemi, HugoShorten, Robert
Permanent link: http://hdl.handle.net/10197/11946
Date: Nov-2019
Online since: 2021-02-15T16:50:55Z
Abstract: This paper deals with the establishment of Input-to-State Stability (ISS) estimates for infinite dimen-sional systems with respect to both boundary and distributed disturbances. First, a new approach isdeveloped for the establishment of ISS estimates for a class of Riesz-spectral boundary control systemssatisfying certain eigenvalue constraints. Second, a concept of weak solutions is introduced in order torelax the disturbances regularity assumptions required to ensure the existence of classical solutions.The proposed concept of weak solutions, that applies to a large class of boundary control systemswhich is not limited to the Riesz-spectral ones, provides a natural extension of the concept of bothclassical and mild solutions. Assuming that an ISS estimate holds true for classical solutions, we showthe existence, the uniqueness, and the ISS property of the weak solutions.
Funding Details: European Commission - European Regional Development Fund
Science Foundation Ireland
Type of material: Journal Article
Publisher: Elsevier
Journal: Automatica
Volume: 109
Copyright (published version): 2019 Elsevier
Keywords: Distributed parameter systemsBoundary control systemsBoundary disturbancesInput-to-state stabilityWeak solutions
DOI: https://doi.org/10.1016/j.automatica.2019.108504
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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