Natural Models for Infinite Dimensional Systems and their Structural Properties

We study here multi-input, multi-output distrib­uted parameter systems. The state space has the structure of a Hilbert space, and the evolution operators form a strongly continuous semigroup. We are thus able to include a large class of systems governed by linear partial differential equations. We present realizability conditions for the input-output maps considered and investigate canonical realizations and their properties. The main mathematical tools are invariant subspace theory in vectorial Hardy Spaces. Using the methods of this particular branch of operator theory we are able to classify the transfer functions considered according to their singularities. This classification is also related to system theoretic concepts and especially to the existence of spectrally minimal realizations. Finally, we discuss the implica­tions of these results to the structure theory of dis­tributed parameter systems, to lumped-distributed network synthesis and delay systems.