An Elementary Result On The Uniform Stability Of A Class Of Continuous Autonomous Systems

Abstract

This paper presents an elementary result on the uniform stability of an equilibrium point for a class of autonomous systems that have an exponentially decreasing factor in their dynamics. The mapping that defines the dynamics may be not Lipschitz so uniqueness of solutions is not assured. Such a class of systems may arise in the stability analysis of some closed-loop control systems, as is the case that leads to this problem, namely, the application of the vertically transverse function approach to the practical point-stabilization of underactuated mechanical systems evolving on Lie groups.