Rational interpolation in H<inf>∞</inf> with a posteriori error bounds

This paper describes a one-step robust identification procedure for linear, time-invariant discrete-time systems. The frequency response of the system at uniformly spaced points are used to find a rational model by interpolation. The poles of the model are chosen to be the n roots of δn, where the value of δ depends on the a priori knowledge of the system. A measure of the margin of stability and the maximum gain of the system are assumed to be known a priori. The measurement noise is arbitrary, but bounded by a known constant. The rational interpolation is proved to be robustly convergent and an explicit worst-case model error bound is determined in terms of the system parameters. This a priori error is shown to be too large and conservative. A tighter error bound is obtained a posteriori, after interpolation by a search method and it is proved to be convergent.