Homogeneous feedback stabilization

1 Introduction and Motivation We address a special case of the general problem of finding continuous feedback laws (that lead to unique solutions) and asymptotically stabilize the origin of (in general) nonlinear smooth systems of the form.x = f (x) + ug(x) with x 2 Rn; u 2 R (1) The purpose of this note is to further popularize the use of feedback laws that are \Delta-homogeneous (i.e. homogeneous w.r.t. a suitable family of dilations) for the global asymptotic stabilization of \Delta-homogeneous control systems, and for the local asymptotic stabilization of general nonlinear systems approximated by homogeneous systems