Published online by Cambridge University Press: 05 May 2022
In this chapter we extend the frequency domain results for i/s/o systems presented in Chapter 11 into analogous frequency domain results for s/s systems. The main definitions are given for general s/s systems, but most of the more specific results require the s/s system to be resolvable (i.e., to have a nonempty resolvent set). We introduce s/s versions of Ω-resolvability, Ω-controllability, Ω-observability, Ω-minimality, Ω-intertwinements, Ω-restrictions, Ω-projections, and Ω-compressions for s/s systems, where Ω is a given nonempty open subset of the complex plane. In this setting the usual (time domain) regularity conditions are less significant. Some of the s/s results are proved directly in the s/s setting, but most of them are reduced to the corresponding i/s/o results by means of i/s/o representations of the given s/s systems.