Classes of well-posed linear systems
In this chapter we recall the notion of w ell-posed linearsystems, which forms the general framework for studying infinite-dimensional systems in a state space con text. In particular, we introduce two important classes of well-posed linear systems which are central in this book and list some of their properties, which will be used in the sequel. Figure 2.1 shows the hierarchy of the various classes of systems that we will encounter in this chapter. Finally, in the last section of this chapter we will introduce several frequency domain spaces and prove a few elementary lemmas which will be used in what follows.
KeywordsHilbert Space Continuous Semigroup Analytic Semigroup Norm Topology Hankel Operator
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