Published online by Cambridge University Press: 05 May 2022
In Chapter 5, we defined various dynamic time domain notions for i/s/o systems, such as reachable and unobservable subspaces, controllability and observability, strong and unobservable invariance, external equivalence, intertwinements, compressions, dilations, restrictions, extensions, and projections. Here, we present frequency domain counterparts of these definitions. One of the four components of a frequency domain trajectory is a constant representing an “initial state,” and the other three components are analytic functions defined on some open subset Ω of the complex plane, representing a “frequency domain state,” a “frequency domain input,” and a “frequency domain output.” By the frequency domain i/s/o system induced by an i/s/o node Σ, we mean the node Σ itself together with the set of all frequency domain trajectories. Some of our frequency domain definitions can be applied to arbitrary i/s/o nodes, but most of the time we assume that Σ is resolvable and that the set Ω on which the trajectories are defined is contained in the resolvent set of Σ.