Well-Posed Linear Systems

Indispensable to all working in systems theory, operator theory, delay equations and partial differential equations.

Olof Staffans (Author)

9780521825849, Cambridge University Press

Hardback, published 24 February 2005

794 pages
24 x 16.5 x 4.6 cm, 1.485 kg

'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

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.

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
7. Feedback
8. Stabilization and detection
9. Realizations
10. Admissibility
11. Passive and conservative scattering systems
12. Discrete time systems
13. Appendix.

Subject Areas: Differential calculus & equations [PBKJ], Calculus & mathematical analysis [PBK]