The authors consider the problem of finding a feedback stabilizing law \(x \to k(x)\) associated with a control system \(x'(t) = f(x(t),u(t))\). Using the concept of positional strategies introduced in the framework of differential games by Krasovskii and Subbotin in 1988, assuming the existence of a Lyapunov Lipschitz function \(V\) defined on the complement of a sufficiently small ball around the origin, they prove the existence of piecewise constant feedback on a partition \(\pi:=\{ t_i \}_{i>0}\) of \([0,+\infty)\) with small enough diameter such that any \(\pi\)-trajectory starting from some neighborhood of a level set of \(V\), remains in this neighborhood until it reaches any given small ball around the origin in finite time. In a second part of the paper the authors prove the existence of a Lyapunov function having the required property to get the previous existence result of ``practical'' stabilization. For this purpose they assume that \(f(\cdot,u)\) is Lipschitz and bounded on any bounded set and that the dynamical system satisfies a controllability property which expresses that a compact set \(A\) exists such that from any initial position in the complement of \(A\) starts a trajectory reaching \(A\) in a finite time. Then they show that there exists a lower semicontinuous Lyapunov function defined as a value function. This function is a solution to the Hamilton-Jacobi equation associated with some appropriate dynamical system. The paper ends with a robustness property of the feedback described in the first statement. Robustness is considered with respect to perturbations due to error measurements on the state position and on its velocity.