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.Read more
- The first book on infinite-dimensional linear systems which are well-posed in a p-integrable setting
- This book contains several original results which have not been published before, and many of the remaining results appear here for the first time in a book
- A number of researchers already use and quote this book (15 citations in ISI Web OS Science in April 2004)
Reviews & endorsements
'What is new, even for most experts in this field, is the detailed treatment of generalised well-posed systems, so-called 'system nodes' … undoubtedly an impressive piece of work … fully deserving of its encyclopaedic pretensions … very well written, with tremendous care given to getting across both the basic ideas of the results and their most general versions … cited literature is incredibly comprehensive, and even most experts in the field will find some hidden gems in the bibliography.' Bulletin of the London Mathematical Society Journal
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- Date Published: February 2005
- format: Hardback
- isbn: 9780521825849
- length: 794 pages
- dimensions: 240 x 165 x 46 mm
- weight: 1.485kg
- availability: In stock
Table of Contents
1. Introduction and overview
2. Basic properties of well-posed linear systems
3. Strongly continuous semigroups
4. The generations of a well-posed linear system
5. Compatible and regular systems
6. Anti-causal, dual and inverted systems
8. Stabilization and detection
11. Passive and conservative scattering systems
12. Discrete time systems
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