This lecture will give a unified approach for semi-global stabilization of nonlinear systems by output feedback. In the case when nonlinear systems are uniformly completely observable (UCO)  and smoothly stabilizable, a solution to semi-global stabilizability of MIMO nonlinear systems is given. It is shown that for MIMO nonlinear systems, global stabilizability via smooth state feedback and uniform observability imply semi-global stabilizability by dynamic a output feedback. This result generalizes the previous theorem established for SISO nonlinear systems. The generalization is made possible by developing a novel, simpler and intuitive argument that involves no intricate Lyapunov functions.

In the 2nd part of this talk, the new method thus developed is used to address the problem of semi-global output feedback stabilization, for a significant class of nonlinear systems that are neither UCO nor smoothly stabilizable.