Optimal reduced-order models for unstable and nonminimum-phase systems

A technique is presented for optimally approximating an unstable and/or nonminimum-phase high-order transfer function by a low-order one which has the same numbers of right half-plane (RHP) poles and zeros as the original system, It is based on representing the denominator and numerator polynomials of a reduced-order transfer function in products of quadratic factors with/without a linear factor. The Routh gamma stability parameters of the linear and quadratic factors are determined such that a frequency-domain L(2)-norm is minimized. The main feature of the proposed approach to finding optimal reduced models is that the stability constraints on the decision parameters become simple bounds. As a result, the numbers of RHP zeros and poles of a reduced model are easily controlled by specifying the numbers of negative Routh gamma parameters for the numerator and denominator polynomials. Moreover, it allows for using a gradient-based optimization technique to find the optimal parameters.