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Linear State/Signal Systems
About this book
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.
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Information
Table of contents
- Cover
- Half-title page
- Series page
- Title page
- Copyright page
- Contents
- Preface
- List of Notations
- 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 A Operators and Analytic Vector Bundles in H-Spaces
- References
- Index