Transfer Function Approximation and Identification Using Magnitude and Phase Criteria

In this paper, we show how convex optimization can be used for model reduction and identification of transfer functions. Two different methods are presented. In the first method magnitude functions are matched, and in the second method phase functions are matched. The weighted error bounds have direct interpretation in a Bode diagram. Both methods are suitable to engineers working with Bode diagrams. Furthermore, we see that transfer functions that have similar magnitude or phase functions also have a small relative H-infinity error under some minimum phase assumptions. The error bounds come from bounds associated with the Hilbert transform operator restricted in its application to rational transfer functions. Two examples are included to illustrate the results. Keywords— Model approximation, model reduction, system identification, magnitude, phase, Hilbert transform, semidefinite programs, KYP lemma, sum of squares decomposition, LMI