Representation of linear dynamical systems by aggregated models

In this paper the problem of representing high-order linear dynamical systems by reduced models is investigated through the use of an aggregation technique. After a brief review of aggregation principles, the general form of an aggregation matrix is established. Many reduced models, already proposed in the literature and retaining the dominant modes of the high-order system, are shown to belong to that class. Finally, a cost function to measure the quality of aggregation is introduced; optimal aggregated models, corresponding to some given deterministic or stochastic input, are then obtained by solving a linear matrix equation.