Lyapunov design of stabilizing state or output feedback

Prof. Laurent Praly, Centre d'Automatique et Informatique

We survey various developments which have been made during the beginning of the nineties about the design of asymptotically stabilizing feedback laws for nonlinear systems. More specifically we restrict our attention to those designs which are obtained by making the time derivative of a Lyapunov function negative along the closed loop solutions. The reported results are related to the following key words~: control Lyapunov functions, robustness of stability, adding integrators, adding integrations, dissipative drift term, driftless systems, dynamics linear in the unmeasured state components.