Feedback stabilization of planar nonlinear systems

Abstract The stabilization of second-order control systems by smooth state feedback is addressed. A reduction procedure proposed in [8] is applied in order to reduce the problem to the stabilization of a first-order control system by a C 2 feedback function. Generic sufficient conditions are given for the solution of the last problem and, by the reduction procedure, of the first problem as well. Counter-examples show that the conditions are not necessary and which kind of pathologies may arise.