Structured frequency weighted model reduction

We consider the problem of reducing a model in a way that preserves a partition of the system states. This is motivated, for instance, in situations where state variables are associated with the topology of a networked system. In earlier work we proposed an LMI method based on block-structured generalized controllability and observability gramians; to make such strategy feasible, coprime factor model reduction was employed. In this paper, we consider the frequency-weighted version of the problem. This is motivated by the usual desire to have model accuracy vary with frequency, but also by the fact that the feasibility of our LMI method can be greatly enhanced through frequency weighting. We show that block-structure can be imposed directly in gramians for frequency weighted problems, and often gives a feasible solution without the need to resort to coprime factors. We also explore the coprime factor version, and give comparisons to other related work in this area.