Given a weakly uniformly globally asymptotically stable closed (not necessarily compact)
set A for a differential inclusion that is defined on Rn, is locally Lipschitz on Rn\A, and
satisfies other basic conditions, we construct a weak Lyapunov function that is locally
Lipschitz on Rn. Using this result, we show that uniform global asymptotic controllability
to a closed (not necessarily compact) set for a locally Lipschitz nonlinear control system
implies the existence of a locally Lipschitz control-Lyapunov function, and from this
control-Lyapunov function we construct a feedack that is robust to measurement noise.