Some Sufficient Conditions for the Global and Local Controllability of Nonlinear Time-Varying Systems

Sufficient conditions are derived for global and local controllability of nonlinear time-varying systems with control appearing linearly. It is shown that the controllability of $\dot x = A(t,x)x + B(t,x)u$ can be related to the controllability of the linear system $\dot x = A(t,z)x + B(t,z)u$, where z belongs to a certain set of continuous vector functions. This result is then used to specify a class of nonlinear systems which are globally controllable.