A Priori Error Bounds for Model Reduction of Interconnected Linear Systems using Robust Performance Analysis

Subsystem reduction of interconnected systems provides a computationally cheap and structure-preserving alternative to direct model order reduction techniques of large-scale systems. Unfortunately, for this method, error bounds for the reduced interconnected system are often difficult to compute or not available. This paper provides an approach to determine an a priori error bound and to give stability guarantees for subsystem reduction of interconnected systems. This is achieved by modeling subsystem reduction errors as an uncertainty such that the structured singular value, a computational tool used in robust control, can be used. A method is provided to compute either a global or a frequency-dependent a priori error bound. Additionally, it is proven that convergence of this method is guaranteed. Finally, the effectiveness of the proposed method is demonstrated by an illustrative example.