Extension of the Belitskii normal form to nonlinear control systems

In this paper, the Belitskii normal form, which is valid for nonlinear vector fields, is extended to nonlinear control systems with a scalar control input, dependent on some physical parameters. The objective is to find suitable local coordinates such that the considered nonlinear system is as simple as possible, in the Poincaré-Dulac sense. As expected, the structure of the normal form is heavily dependent on the properties of the nominal linear approximation.