Generalized homogeneous approximations and the global stabilization of nonlinear systems

We introduce a new notion of generalized homogeneous approximation at the origin and at infinity which extends the classical notions. Homogeneous systems in the generalized sense are a very large class of nonlinear systems, including (lower and upper) triangular systems. Exploiting this extension we give basic results concerning stabilization and robustness of nonlinear systems which have a generalized homogeneous approximation at zero and at the origin.