Output Stabilization via Nonlinear Luenberger Observers

The present paper addresses the problem of existence of an (output) feedback law to the purpose of asymptotically steering to zero {prescribed outputs}, while keeping all state variables bounded, for any initial conditions in a given compact set. The problem can be viewed as an extension of the classical problem of semi-globally stabilizing the trajectories of a controlled system to a compact set. The problem also encompasses a version of the classical problem of output regulation. Under only a {em weak minimum phase} assumption, it is shown that there exists a controller solving the problem at hand. The paper is deliberately focused on theoretical results regarding the existence of such controller. Practical aspects involving the design and the implementation of the controller are left to a forthcoming work.