Local and global controllability for nonlinear systems

Abstract A technique to study local and global controllability properties for a wide class of nonlinear systems is presented. In addition to an extensive study of systems on R 2 we propose — as an application of our method — a new criterion for global controllability of systems with polynomial drift term, defined on R n. In the case of linear systems, the criterion reduces to the classical Kalman condition. A study of local controllability at the equilibrium point of the drift term of systems defined on R 2 enables us not only to rederive a local controllability result derived by Hermes [4,5], but also to extend this result when no assumptions are made on the boundedness of the controls.