The continuous dependence of the solution of the controllability problem on the initial and the terminal states for the triangular nonlinearizable systems

Sufficient conditions for the existence of a family of controls $u_{(x^0, x^T)}(\cdot)$, steering the state $x^0 \in{\mathbf R}^n$ into the state $x^T\in{\mathbf R}^n$, for all $x^0\in{\mathbf R}^n$ and $x^T\in{\mathbf R}^n$, and continuously depending on $x^0\in{\mathbf R}^n$ and $x^T\in{\mathbf R}^n$, are given for a class of triangular systems whose trajectories, in general, can not be mapped by a diffeomorphism onto the trajectories of a linear canonical system. As a corollary, the complete controllability of the uniformly bounded perturbations of this class is obtained under the global Lipschitz condition for the right-hand side with respect to $x$ and $u$.