Linear State/Signal Systems

Discover a new approach to observing and controlling linear systems whose inputs and outputs are not fixed in advance.

Damir Z. Arov (Author), Olof J. Staffans (Author)

9781316519677, Cambridge University Press

Hardback, published 26 May 2022

1080 pages
25.1 x 17.4 x 6.1 cm, 1.877 kg

The authors explain in this work a new approach to observing and controlling linear systems whose inputs and outputs are not fixed in advance. They cover a class of linear time-invariant state/signal system that is general enough to include most of the standard classes of linear time-invariant dynamical systems, but simple enough that it is easy to understand the fundamental principles. They begin by explaining the basic theory of finite-dimensional and bounded systems in a way suitable for graduate courses in systems theory and control. They then proceed to the more advanced infinite-dimensional setting, opening up new ways for researchers to study distributed parameter systems, including linear port-Hamiltonian systems and boundary triplets. They include the general non-passive part of the theory in continuous and discrete time, and provide a short introduction to the passive situation. Numerous examples from circuit theory are used to illustrate the theory.

1. Introduction and overview
2. State/signal systems: trajectories, transformations, and interconnections
3. State/signal systems: dynamic and frequency domain properties
4. Input/state/output representations
5. Input/state/output systems: dynamic and frequency domain properties
6. Bounded input/state/output systems in continuous and discrete time
7. Bounded state/signal systems in continuous and discrete time
8. Semi-bounded input/state/output systems
9. Semi-bounded state/signal systems
10. Resolvable input/state/output and state/signal nodes
11. Frequency domain input/state/output systems
12. Frequency domain state/signal systems
13. Internally well-posed systems
14. Well-posed input/state/output systems
15. Well-posed state/signal systems
Appendix
Operators and analytic vector bundles in H-spaces
References
Index.

Subject Areas: Differential calculus & equations [PBKJ], Number systems [PBCN]