Structure Preserving Model Order Reduction of Linear Time-Invariant Control Systems

In this contribution a survey will be presented on the requirements of projection-based procedures of model order reduction of large-scale linear time-invariant systems to preserve certain structural properties like asymptotic stability, complete controllability, or complete observability. Also “algebraic” properties are discussed like steady-state accuracy, vanishing equation residuum, or separation of controller/observer design. The conditions on the projection matrices are shown explicitly. Some of these conditions coincide with respect to different structural properties. Additionally, it can be shown that truncation methods which are based on decoupling either of eigenmodes or of controllability and observability Gramian matrices preserve asymptotic stability, complete controllability, and complete observability always.