Necessary and Sufficient Condition for Global Controllability of Planar Affine Nonlinear Systems

In this correspondence, we will investigate the global controllability of general planar affine nonlinear systems, and present a simple necessary and sufficient condition for global controllability. The analysis is carried out in detail, which is based on some basic facts in planar topology such as the Jordan curve Theorem, and in the geometrical theory of ordinary differential equations including the Poincare-Bendixson Theorem. Furthermore, we will also discuss the global controllability for higher dimensional affine nonlinear system with a triangular-like structure.