Optimal $\mathcal{H}_2$ Model Reduction for Large Scale MIMO Systems via Tangential Interpolation

Abstract

We consider the optimal $\mathcal{H}_2$ model reduction for large scale multi-input multi-output systems via tangential interpolation. Specifically, we prove that for general multi-input multi-output systems, the tangential interpolation-based optimality conditions and the gramian-based optimality conditions are equivalent. Based on the tangential interpolation, a fast algorithm is proposed for the optimal $\mathcal{H}_2$ model reduction. Numerical examples are presented to demonstrate the approximation accuracy and computational efficiency of the proposed algorithm.