A constructive approach to local stabilization of nonlinear systems by dynamic output feedback

The note considers the problem of local stabilization of nonlinear systems by dynamic output feedback. A new concept, namely, local uniform observability of feedback control law, is introduced. The main result is that if a nonlinear system is Nth-order approximately stabilizable by a locally uniformly observable state feedback, then it is stabilizable by dynamic output feedback. Based on the approximate stability, a constructive method for designing dynamic compensators is presented. The design of the dynamic compensators is beyond the separation principle and can handle systems whose linearization might be uncontrollable and/or unobservable. An example of nonminimum phase nonlinear systems is presented to illustrate the utility of the results.