Nonlinear locally Lipschitz output regulation in presence of non-hyperbolic zero-dynamics

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 output regulation by output feedback. We show how it is possible to design locally Lipschitz internal model-based regulator under conditions which only rely upon a partial detectability assumption on the controlled plant, by obtaining a robust stabilizing paradigm which is not based on design of observers and separation principles.