Book contents
- Frontmatter
- Contents
- Preface
- 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 Input/State/Output 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
14 - Well-Posed Input/State/Output Systems
Published online by Cambridge University Press: 05 May 2022
- Frontmatter
- Contents
- Preface
- 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 Input/State/Output 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
Summary
This chapter is devoted to the study of well-posed i/s/o systems. These systems are assumed to be solvable and to satisfy a well-posedness condition that guarantees the existence of a unique future generalized trajectory for any given initial state and input function that belongs locally to L2. Although it is not obvious from the definition, every well-posed i/s/o system is internally well-posed, i.e., it has a nonempty resolvent set-and its main operator generates a C0 semigroup. Semi-bounded i/s/o systems are well-posed. The class of well-posed i/s/o systems is the largest class in this book for which can to prove connections between time and frequency domain results that are analogous to those established in Chapter 8 for the class of semi-bounded i/s/o systems. At the end of this chapter we define the notion of a scattering passive system, and show that scattering passive systems are well-posed. A scattering passive system is characterized by the fact that it is regular, and its system operator is maximally scattering dissipative. Well-posed s/s systems are discussed in Chapter 15.
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- Linear State/Signal Systems , pp. 816 - 906Publisher: Cambridge University PressPrint publication year: 2022