Well-posed linear systems / Olof Staffans.

Format:

Book

Author/Creator:

Staffans, Olof J., 1947- author.

Series:

Encyclopedia of mathematics and its applications ; v. 103.

Encyclopedia of mathematics and its applications ; volume 103

Language:

English

Subjects (All):

Linear systems.

System theory.

Physical Description:

1 online resource (xviii, 776 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2005.

Language Note:

English

Summary:

Many infinite-dimensional linear systems can be modelled in a Hilbert space setting. Others, such as those dealing with heat transfer or population dynamics, need to be set more generally in Banach spaces. This is the first book dealing with well-posed infinite-dimensional linear systems with an input, a state, and an output in a Hilbert or Banach space setting. It is also the first to describe the class of non-well-posed systems induced by system nodes. The author shows how standard finite-dimensional results from systems theory can be extended to these more general classes of systems, and complements them with new results which have no finite-dimensional counterpart. Much of the material presented is original, and many results have never appeared in book form before. A comprehensive bibliography rounds off this work which will be indispensable to all working in systems theory, operator theory, delay equations and partial differential equations.

Contents:

1. Introduction and overview

2. Basic properties of well-posed linear systems

3. Strongly continuous semigroups

4. The generators of a well-posed linear system

5. Compatible and regular systems

6. Anti-casual, dual, and inverted systems

7. Feedback

8. Stabilization and detection

9. Realizations

10. Admissibility

11. Passive and conservative scattering systems

12. Discrete time systems

App. 1. Regulated functions

App. 2. The positive square root and the polar decomposition

App. 3. Convolutions

App. 4. Inversion of block matrices.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 750-766) and index.

ISBN:

1-107-13780-2

1-280-43113-X

9786610431137

0-511-17131-5

0-511-19701-2

0-511-08208-8

0-511-54319-0

0-511-29840-4

0-511-08163-4

OCLC:

171136927