H2-Optimal Model Reduction with Higher-Order Poles

We revisit the problem of approximating a multiple-input multiple-output (MIMO) p×m rational transfer function H(s) of high degree by another p×m rational transfer function b H(s) of much smaller degree, so that the H2 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 H2 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.