  We consider the time optimal stabilization problem for a nonlinear control
system $\dot x=f(x,u)$. Let $\tau(y)$ be the minimum time needed to steer the
system from the state $y\in\R^n$ to the origin, and call $\A(T)$ the set of
initial states that can be steered to the origin in time $\tau(y)\leq T$. Given
any $\ve>0$, in this paper we construct a patchy feedback $u=U(x)$ such that
every solution of $\dot x=f(x, U(x))$, $x(0)=y\in \A(T)$ reaches an
$\ve$-neighborhood of the origin within time $\tau(y)+\ve$.
