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

TL;DR

This paper establishes that for general time-varying systems, the existence of an Output Robust Control Lyapunov Function guarantees the design of continuous time-varying feedback stabilizers ensuring output asymptotic stability, generalizing previous autonomous system results.

Contribution

It extends classical feedback stabilization results to broader time-varying systems using Control Lyapunov Functions.

Findings

Existence of an Output Robust Control Lyapunov Function implies stabilizer design.

Continuous time-varying feedback stabilizers can be constructed for such systems.

The results generalize known autonomous system stabilization theorems.

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.