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In this paper we present a general tool to handle the presence of zerodynamics which are asymptotically but not locally exponentially stable inproblems of robust nonlinear stabilization by output feedback. We show how itis possible to design locally Lipschitz stabilizers under conditions which onlyrely upon a partial detectability assumption on the controlled plant, byobtaining a robust stabilizing paradigm which is not based on design ofobservers and separation principles. The main design idea comes from recentachievements in the field of output regulation and specifically in the designof nonlinear internal models.

Robust Asymptotic Stabilization of Nonlinear Systems with Non-Hyperbolic Zero Dynamics