Aggregation of a class of linear, interconnected dynamical systems

We introduce the notion of a "meaningful" average of a collection of dynamical systems as distinct from an "ensemble" average. Such a notion is useful for the study of a variety of dynamical systems such as traffic flow, power systems, and econometric systems. We also address the associated issue of the existence and computation of such an average for a class of interconnected, linear, time invariant dynamical systems. Such an "average" dynamical system is not only attractive from a computational perspective, but also represents the average behavior of the interconnected dynamical system. The problem of analysis and control of hierarchical, large scale control systems can be simplified by approximating the lower level dynamics of such systems with such an average dynamical system.