A computer-aided approach for Routh-Pade approximants

A computer-aided approach (based on geometric programming) to approximate a given high-order transfer function by a low-order one is presented. The method guarantees that a stable system will always be reduced to a stable model only. The effects of both time moments and Markov parameters are considered with a view to ensure overall time response approximation. The proposed method is essentially a nonlinear optimization procedure in which the errors between (r+1)st, ( r+2)nd, . . . time moments/Markov parameters of the model and the respective time moments/Markov parameters of the system are minimized starting from a known Hurwitz denominator polynomial, while preserving stability and fully retaining the first r time moments/Markov parameters of the system, where r denotes the order of the reduced-order model