Model reduction for controller design for infinite-dimensional systems

The main aim of this thesis is, as the title suggests, the presentation of results on model reduction for controller design for infinite-dimensional systems. The obtained results are presented for both discrete-time systems and continuous-time systems. They are perfect generalizations of the corresponding finite-dimensional ones. The model reduction for controller design method is illustrated by a controller design for a beam. Along the way we generalized several important theorems and introduced a few promising new concepts. Arguably the most important theorem that we generalize is that on the existence of (strongly) coprime factorizations. The results in this thesis solve this long outstanding problem for which many partial results exist in the literature. The most important new concept resulting from this Ph.D. work is probably that of a (distributional) resolvent linear system. As shown in this thesis many systems described by partial differential equations fall into this class of systems and one can reasonably easily prove theorems for this class of systems. That this new concept brings together well-established concepts such as distribution semigroups, the Cayley transform and nonhomogeneous elliptic boundary value problems strengthens our belief that we have discovered an important new class of systems.