Backstepping Design for Output Feedback Stabilization for a Class of Uncertain Systems using Dynamic Extension

We revisit the backstepping approach. We show how bounded globally asymptotically stabilizing output feedbacks can be constructed for a family of nonlinear systems. The approach relies on the introduction of a dynamic extension and a converging-input-converging-state assumption. The technique presents several advantages. It provides control laws whose expressions are simple. It makes it possible to stabilize systems in the presence of certain types of uncertain terms which prevent the use of the classical backstepping technique. It applies in notable cases where only part of the state variable is measured.