On system-identification and robust control on Hardy-Sobolov space

The paper presents a systematic methodology that integrates input-output data with robust control, by interfacing it with system identification, for systems belonging to Hardy-Sobolov space. The inner-product structure of the space makes it attractive for both identification and robust control design of infinite dimensional systems. The class of infinite-dimensional systems considered do not allow for an arbitrarily close finite-dimensional parametrization during the identification stage, which results in unmodeled dynamics bounded by the Sobolov norm in addition to parametric uncertainty. Robust control design has to thus explicitly take this structure into consideration. We present recursive algorithms for system identification to estimate unmodeled dynamics and parametric uncertainty. The robustness analysis and synthesis results are developed for these type of uncertainties