Control Lyapunov Functions and Stabilization by Means of Continuous Time-Varying Feedback

Abstract

For a general time-varying system, we prove that existence of an "Output Robust Control Lyapunov Function" implies existence of continuous time-varying feedback stabilizer, which guarantees output asymptotic stability with respect to the resulting closed-loop system. The main results of the present work constitute generalizations of a well-known result towards feedback stabilization due to J. M. Coron and L. Rosier concerning stabilization of autonomous systems by means of time-varying periodic feedback.

Submitted for possible publication to ESAIM Control, Optimisation and Calculus of Variations