Hierarchically consistent control systems

In hierachical systems, higher levels of the hierarchy utilise coarser system models by aggregating the detailed lower level models. In this layered control paradigm, the notion of hierarchical consistency ensures the implementation of high level objectives by the lower level system. In this paper, we define a notion of modeling hierarchy for continuous control systems and obtain characterizations for hierarchically consistent linear systems with respect to controllability objectives. As an interesting by-product, we obtain a hierarchical controllability criterion for linear systems from which we recover the best known controllability algorithm from numerical linear algebra