Linear and nonlinear algorithms for identification in H∞ with error bounds

In this paper, a linear and a nonlinear algorithm are presented for the problem of system "identification in H^∞", posed by Helmicki, Jacobson and Nett. We derive some error bounds for the linear algorithm which indicate that if the model error is not too high, then this algorithm has good guaranteed error properties. The linear algorithm requires only FFT (fast Fourier transform) computations. A nonlinear algorithm, which requires an additional step of solving a Nehari best approximation problem, is also presented that has the robust convergence property.