PASSIVITY, FEEDBACK EQUIVALENCE, AND THE GLOBAL STABILIZATION OF MINIMUM PHASE NONLINEAR-SYSTEMS

In this paper, we derive conditions under which a nonlinear system can be rendered passive via smooth state feedback and we show that, as in the case linear systems, that is possible if and only if the system in question has relative degree 1 and is weakly minimum phase. Then, we prove that weakly minimum phase nonlinear systems having relative degree 1 can be globally asymptotically stabilized by smooth state feedback, provided that suitable controllability-like rank conditions are satisfied. This result incorporates and extends a number of stabilization schemes recently proposed in the literature for global asymptotic stabilization of certain classes of nonlinear systems.