Robust asymptotic stabilization of nonlinear systems with non-hyperbolic zero dynamics: Part I

In this paper we present a general tool to handle the presence of zero dynamics which are asymptotically, but not locally exponentially, stable in problems of robust nonlinear stabilization by output feedback. We show how it is possible to design locally Lipschitz stabilizers under conditions which do not rely upon any observability assumption on the controlled plant, by thus obtaining a robust stabilizing paradigm which is not based on design of observers and separation principles. The main design idea comes from recent achievements in the field of output regulation and specifically in the design of nonlinear internal models. In this sense the results presented in this paper also complement in a non trivial way a certain number of works recently proposed in the field of output regulation by presenting meaningful conditions under which a locally Lipschitz regulator exists. The present work is complemented by a part II paper submitted to this conference ([11]) in which possible applications of the presented tool in the context of the robust stabilization and regulation of minimum-phase nonlinear systems and robust nonlinear separation principle are presented.