Algorithms for identification in H_∞ with unequally spaced function measurements

Abstract

Worst-case identification in H_∞is considered in the situation in which corrupted frequency response measurements are available at an arbitrary set of frequencies. Two new classes of algorithms are presented: one yields polynomial models directly, the other is a two-stage algorithm producing rational models. Each has improved convergence rates for the class of exponentially stable discrete-time systems (with errors typically O(ε)+ O(Δ^r) for arbitrarily large r, where ε is the noise level and Δ is the maximum spacing between identification points). A numerical example is given.