LMI approach to structured model reduction via coprime factorizations

We discuss dynamic model reduction methods which preserve a certain structure in the underlying system. Specifically, we consider the situation where the reduction must be consistent with a partition of the system states. This is motivated by, for instance, situations where state variables are associated with the topology of a networked system, and the reduction should preserve this. We build on the observation that imposing block structure to generalized controllability and observability gramians automatically yields such state partitioned model reduction. The difficulty lies in ensuring feasibility of the resulting Lyapunov inequalities, which is in general very restrictive. To overcome this, we consider coprime factor model reduction. We derive an LMI characterization of expansive coprime factorizations that preserve structure, and use this to build a more flexible method for structured model reduction. An example is given to illustrate the method.