  This paper studies the use of vector Lyapunov functions for the design of
globally stabilizing feedback laws for nonlinear systems. Recent results on
vector Lyapunov functions are utilized. The main result of the paper shows that
the existence of a vector control Lyapunov function is a necessary and
sufficient condition for the existence of a smooth globally stabilizing
feedback. Applications to nonlinear systems are provided: simple and easily
checkable sufficient conditions are proposed to guarantee the existence of a
smooth globally stabilizing feedback law. The obtained results are applied to
the problem of the stabilization of an equilibrium point of a reaction network
taking place in a continuous stirred tank reactor.
