H∞ identification of stable LSI systems: a scheme with direct application to controller design

In this paper several techniques are given for the identification of stable LSI discrete time systems from input-output data. Explicit H_∞ norm error bounds are given and convergence in the noise free and the uniformly bounded deterministic noise case are established. The assumptions made on the unknown system are minimal and are limited throughout the paper to a lower bound on the decay rate of the unknown system and an upper bound on the gain of the unknown system. Given this information an experiment and a construction are specified: the experiment involves obtaining a specified number of frequency measurements of the unknown systems at a set of specified frequencies; the construction uses this experimental data to generate an identified model with prescribed H_∞ norm error tolerance to the unknown system. The resulting model identification process is highly efficient from a computational point of view.