A class of controllable nonlinear systems

Sufficient conditions for global and local controllability of the nonlinear system
\frac{d}{dt}x(t) = A(t,x(t), u(t))x(t) + B(t)u(t) + f(t,x(t), u(t))
and its perturbed system are given. These conditions extend some previous results through the removal of certain boundedness conditions involving the functions (
A,f
) and their partial derivatives.