Global stabilizability and observability imply semi-global stabilizability by output feedback

We show that smooth global �or even semi-global � stabilizability and uniform complete observability are su�cient properties to guarantee semi-global stabilizability by dynamic output feedback for continuous-time nonlinear systems. Keywords: Output feedback, Semi-global stabilizability, Uniform complete observability. Notation: � Let �0 � denote the number of the di�erential equation: _x = f�x�: �0� For any continuous function V: A! R, with A � R p,we denote by _ V �0 � the Lie derivative ofV along the �eld f when it exists on A, i.e.: _V �0��x � = lim t!0 When V is continuously di�erentiable we have trivially: � j�jdenotes the Euclidean norm. � A function f: A! R+, with A � R p, is said to be proper on A if