A canonical form for a class of noncontrollable nonlinear systems

We address the problem of giving a new canonical form for a class of (time varying) nonlinear noncontrollable systems. We define and solve the partial linearization problem (PLP) by static state feedback. Our notion of linearization is weaker than the one found in the literature, since we want to transform the given system to a controllable linear system that is affected by a (perhaps nonlinear) autonomous system, which plays the role of its noncontrollable part. For the class of nonlinear systems for which the PLP is solvable, we show that the influence of the noncontrollable part in the linear part can be always removed by a convenient static state feedback. In particular, a new canonical form for this class of noncontrollable nonlinear systems is obtained.