Exact and approximate feedback linearization without the linear controllability assumption

The feedback linearization problem of nonlinear control systems has been solved in the literature under the assumption that the nonlinear system is linearly controllable. In this paper, the assumption of linear controllability is removed; necessary and sufficient conditions are given through Lie orbital symmetries, thus giving a geometric characterization of the problem in the analytic case. Both the exact and the approximate linearization problems are considered in the analytic case.