Completely feedback linearizable families for uncertain nonlinear systems

We characterize the whole class of vector fields that can be linearized by a given nominal state transformation and a feedback linearizing controller. The necessary and sufficient condition for a given uncertain vector field to be so-called "completely linearizable by the nominal coordinate transformation" is given in terms of Lie bracket of uncertain vector fields and some suitable vector fields of the nominal system. If an uncertain nonlinear system satisfies the proposed condition, then this nonlinear system can be transformed into a linear system with unknown parameters and consequently the wide-spread robust control technique for linear systems can be applied to stabilize the uncertain nonlinear system.