Balanced model reduction with guaranteed performance in frequency ranges

We propose a model reduction method that has less reduction error in desired frequency range. It is guaranteed that the reduced order model is asymptotically stable and balanced. The reduced order model has no error at the specified frequency (w₁), and L_∞ -norm bound on the reduction error can be obtained. By the suitable choice of w₁, we can obtain a reduced order model which is more accurate in the specific frequency range. This method includes truncated balanced realization and singular perturbation model reduction as special cases