Non-well-posed infinite-dimensional linear systems

Mark Opmeer; Ruth F Curtain

doi:10.1109/CDC.2006.377352

Non-well-posed infinite-dimensional linear systems

Research output: Chapter in Book/Report/Conference proceeding › Chapter in a published conference proceeding

Abstract

We provide an abstract framework for infinite-dimensional linear systems that are not necessarily well-posed in the standard L2 sense. One example of a system that is not well-posed but does fit into the new abstract framework is the heat equation with Dirichlet control and Neumann observation. The new abstract framework presented is based on distribution theory. We discuss problems such as: the linear quadratic regulator problem, coprime factorization, robustly stabilizing controllers with respect to factor perturbations and LQG-balanced model reduction. All these problems admit a satisfactory solution at the level of generality of the new abstract framework

Original language	English
Title of host publication	Proceedings of the 45th IEEE Conference on Decision and Control
Publisher	IEEE
Pages	4694 - 4699
Number of pages	6
ISBN (Print)	1-4244-0171-2
DOIs	https://doi.org/10.1109/CDC.2006.377352
Publication status	Published - 2006
Event	45th IEEE Conference on Decision and Control (CDC2006) - San Diego, USA United States Duration: 13 Dec 2006 → 15 Dec 2006

Conference

Conference	45th IEEE Conference on Decision and Control (CDC2006)
Country/Territory	USA United States
City	San Diego
Period	13/12/06 → 15/12/06

Access to Document

10.1109/CDC.2006.377352

Cite this

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title = "Non-well-posed infinite-dimensional linear systems",

abstract = "We provide an abstract framework for infinite-dimensional linear systems that are not necessarily well-posed in the standard L2 sense. One example of a system that is not well-posed but does fit into the new abstract framework is the heat equation with Dirichlet control and Neumann observation. The new abstract framework presented is based on distribution theory. We discuss problems such as: the linear quadratic regulator problem, coprime factorization, robustly stabilizing controllers with respect to factor perturbations and LQG-balanced model reduction. All these problems admit a satisfactory solution at the level of generality of the new abstract framework",

author = "Mark Opmeer and Curtain, {Ruth F}",

year = "2006",

doi = "10.1109/CDC.2006.377352",

language = "English",

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pages = "4694 -- 4699",

booktitle = "Proceedings of the 45th IEEE Conference on Decision and Control",

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note = "45th IEEE Conference on Decision and Control (CDC2006) ; Conference date: 13-12-2006 Through 15-12-2006",

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T1 - Non-well-posed infinite-dimensional linear systems

AU - Opmeer, Mark

AU - Curtain, Ruth F

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N2 - We provide an abstract framework for infinite-dimensional linear systems that are not necessarily well-posed in the standard L2 sense. One example of a system that is not well-posed but does fit into the new abstract framework is the heat equation with Dirichlet control and Neumann observation. The new abstract framework presented is based on distribution theory. We discuss problems such as: the linear quadratic regulator problem, coprime factorization, robustly stabilizing controllers with respect to factor perturbations and LQG-balanced model reduction. All these problems admit a satisfactory solution at the level of generality of the new abstract framework

AB - We provide an abstract framework for infinite-dimensional linear systems that are not necessarily well-posed in the standard L2 sense. One example of a system that is not well-posed but does fit into the new abstract framework is the heat equation with Dirichlet control and Neumann observation. The new abstract framework presented is based on distribution theory. We discuss problems such as: the linear quadratic regulator problem, coprime factorization, robustly stabilizing controllers with respect to factor perturbations and LQG-balanced model reduction. All these problems admit a satisfactory solution at the level of generality of the new abstract framework

U2 - 10.1109/CDC.2006.377352

DO - 10.1109/CDC.2006.377352

M3 - Chapter in a published conference proceeding

SN - 1-4244-0171-2

SP - 4694

EP - 4699

BT - Proceedings of the 45th IEEE Conference on Decision and Control

PB - IEEE

T2 - 45th IEEE Conference on Decision and Control (CDC2006)

Y2 - 13 December 2006 through 15 December 2006

ER -

Non-well-posed infinite-dimensional linear systems

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