H-2-OPTIMAL MODEL REDUCTION WITH HIGHER-ORDER POLES

摘要

We revisit the problem of approximating a multiple-input multiple-output p x m rational transfer function H(s) of high degree by another p x m rational transfer function (H) over cap (s) of much smaller degree, so that the H-2-norm of the approximation error is minimized. We show that in the general case of higher-order poles in the reduced-order model, called the defective case, the stationary points of the H-2-norm of the approximation error can still be characterized by tangential interpolation conditions. We also indicate that the sensitivity of the solution of this problem depends on the parameterization used.