Abstract
It is known that if the linearized model of a nonlinear system is controllable then the original nonlinear system is also controllable near the origin. In this paper, we discuss the size of the null controllability region of a nonlinear system by means of a functional analysis under the condition that the linearized system is controllable at the origin, and derive the quantitative estimation for this size. As no extra assumption is added to the system except that the linearized system is controllable, this result can be applicable for a large class of nonlinear systems. When the null controllability region coincides with the whole of the state space, the system is completely controllable. Therefor, some sufficient controllability conditions are derived for nonlinear systems from this quantitative result.
