The stabilization problem of the affine control system $\dot x = f_0 (x) + u_1 f_1(x)+..+u_m f_m(x)$ with homogeneous functions $f_i$ is studied. This class of systems is of interest due to the robust properties of homogeneity and the fact that many affine systems can be approximated by or transformed to the class under consideration. An advantage of the introduced design method is that the tuning rules are presented in the form of linear matrix inequalities. Performance of the approach is illustrated by a numerical example.