Stability and Stabilization of Homogeneous Systems Depending on a Parameter

This technical note deals with the Lyapunov stability and stabilization of nonlinear homogeneous systems depending on a parameter. We give a new method for proving global stability and stabilization by using a continuous topological deformation which preserves the stability. The proposed results use a condition based on a well known topological lemma, called the tube lemma. To illustrate these results, we study finite time robust stabilization of the chain of integrators.