Non-well-posed infinite-dimensional linear systems

Author

Opmeer, Mark R. ; Curtain, Ruth F.

Author_Institution

Dept. of Math., Groningen Univ.

fYear

2006

fDate

13-15 Dec. 2006

Firstpage

4694

Lastpage

4699

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

Keywords

linear quadratic control; linear systems; matrix decomposition; multidimensional systems; perturbation techniques; reduced order systems; robust control; Dirichlet control; LQG-balanced model reduction; Neumann observation; coprime factorization; distribution theory; factor perturbations; heat equation; infinite-dimensional linear systems; linear quadratic regulator problem; robustly stabilizing controllers; Control systems; Frequency domain analysis; Linear systems; Partial differential equations; Reduced order systems; Regulators; Robust control; Temperature control; Topology; USA Councils;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2006 45th IEEE Conference on

Conference_Location

San Diego, CA

Print_ISBN

1-4244-0171-2

Type

conf

DOI

10.1109/CDC.2006.377352

Filename

4177124