"Fast" set membership H∞ identification from frequency-domain data

H
_∞
identification of model sets for linear, time-invariant, discrete-time, BIBO stable SISO systems is here considered, assuming a known bound on the transfer-function derivative magnitude as prior information on the system to be identified. Experimental information consists of a finite number of measurements in the frequency domain, corrupted by a pointwise bounded additive noise. The aim is to deliver a model set, consisting in a nominal model and frequency-domain bounds, whose size measures the uncertainty about the system to be identified. In the present paper, a new interpolatory algorithm is derived by solving a linear programming problem, aiming to approximate the centers of the frequency-domain uncertainty regions. Moreover, frequency shaped bounds on the identification uncertainty are obtained. One of the most interesting features of the results presented here is that using prior assumptions on transfer-function derivative magnitude, frequency-shaped model sets can be obtained, with computational effort significantly lower than in the cases where other types of priors are assumed on the plant to be identified.