Published online by Cambridge University Press: 05 May 2022
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.