From local to global asymptotic stabilizability for weakly contractive control systems

TL;DR

This paper proves that for weakly contractive control systems, local asymptotic stabilizability guarantees global stabilizability via dynamic feedback, extending classical results with a new geometric approach.

Contribution

It establishes a link between local and global stabilizability for weakly contractive systems using a novel geometric method.

Findings

Local stabilizability implies global stabilizability for these systems.

Dynamic state feedback can achieve global stabilization.

The approach connects with Jurdjevic and Quinn's method.

Abstract

A nonlinear control system is said to be weakly contractive in the control if the flow that it generates is non-expanding (in the sense that the distance between two trajectories is a non-increasing function of time) for some fixed Riemannian metric independent of the control. We prove in this paper that for such systems, local asymptotic stabilizability implies global asymptotic stabilizability by means of a dynamic state feedback. We link this result and the so-called Jurdjevic and Quinn approach.