  The solution of the global controllability problem is obtained for a class of
the triangular systems of O.D.E. that are not feedback linearizable. The
introduced class is a generalization of the classes of triangular systems
investigated before. The solution of the problem is based on the approach
proposed in another work [18] devoted to the triangular systems of the Volterra
equations and written jointly with W.H. Schmidt by the current authors. This
yields the same properties of the considered class of triangular systems as
those established in [18] for the Volterra systems. As well as in [18], for the
current class of triangular systems, it is proven that there exists a family of
continuous controls that solve the global controllability problem for the
considered class and continuously depend on the initial and the terminal
states. As well as in [18], this implies the global controllability of the
bounded perturbations of the current class. In contrast with [18], to prove the
existence of the desired family of open-loop controls, we construct a family of
closed-loop ones each of which steers the corresponding initial state into an
appropriate neighborhood of an appropriate terminal point.
