On the global controllability for a class of 3-dimensional nonlinear systems with two inputs

This paper discusses the global controllability for a class of 3-dimensional nonlinear systems with two inputs. Firstly, we retrospect the difficulty and progress for the study of the global controllability of higher dimensional nonlinear systems. Secondly, we present a necessary and sufficient condition for the global controllability of 3-dimensional nonlinear system with two inputs under some assumptions. All conditions are imposed on the structure of the system only. Finally, we give some examples to show the application of our results.