Dual inclusion principle for reduced order model systems

An input-state-output dual inclusion is proposed for dual reduced order model systems in this paper. For restriction and aggregation as inclusion principle special cases, dual relationships of these two special contraction conditions are formulated for a linear time invariant balanced original system and its dual system. It is shown that, if dual inclusion conditions are satisfied for both the original system and its dual system, an ideal reduced order model of the system can be contracted perfectly by choosing only one type of contractions (restrictions or aggregations) from these two systems in the same time. Usually, an imperfect contraction can be applied to model reductions and can give an approximate reduced order model for the balanced original system.