  In this paper we estimate the minimal controllability time for a class of
non-linear control systems with a bounded convex state constraint. An explicit
expression is given for the controllability time if the image of the control
matrix is of co-dimension one. A lower bound for the controllability time is
given in the general case. The technique is based on finding a lower dimension
system with the similar controllability properties as the original system. The
controls corresponding to the minimal time, or time close to the minimal one,
are discussed and computed analytically. The effectiveness of the proposed
approach is illustrated by a few examples.
