Robust identification and interpolation in H∞

Abstract

We consider system identification in H_∞ in the framework proposed by Helmicki, Jacobson and Nett. An algorithm using the Jackson polynomials is proposed that achieves an exponential convergence rate for exponentially stable systems. It is shown that this, and similar identification algorithms, can be successfully combined with a model reduction procedure to produce low-order models. Connections with the Nevanlinna-Pick interpolation problem are explored, and an algorithm is given in which the identified model interpolates the given noisy data. Some numerical results are provided for illustration. Finally, the case of unbounded random noise is discussed and it is shown that one can still obtain convergence with probability 1 under natural assumptions.