Nonlinear Output Regulation and Cross-terms compensation

In this paper we survey the results recently obtained previously by the author in the context of output regulation and we frame them in a broader context of set stabilization by output feedback. The peculiarity of the set stabilization framework which is here formulated is given by the presence of non-vanishing cross-terms between zero- and output-dynamics. We show how the mathematical tools previously developed allow for the synthesis of a robust control law which is not inspired by certainty equivalence principles. As new application of the tools we show how a problem of output feedback asymptotic stabilization with zero dynamics which are not exponentially stable can be handled by means of high-gain output feedback.