Stability of homogeneous nonlinear systems with sampled-data inputs

The main goal of this article is to use properties of homogeneous systems for addressing the problem of stability for a class of nonlinear systems with sampled-data inputs. This nonlinear strategy leads to several kinds of stability, i.e. local asymptotic stability, global asymptotic stability or global asymptotic set stability, depending on the sign of the degree of homogeneity. The results are illustrated with the case of the double integrator.