This paper is concerned with the impulsive control problem $$ dot{x}(t) = f(t, x) + g(t, x)dot{u}(t), t in [0, T], x(0) = overline{x}, $$ where u is a possibly discontinuous control function of bounded variation, $f : R imes R^n mapsto R^n$ is a bounded and Lipschitz continuous function, and $g : R imes R^n mapsto R^n$ is continuously differentiable w.r.t. the variable x and satisfies $mid$g(t,cdot) - g(s,cdot)$mid$ leq phi(t) - phi(s)$, for some increasing function $phi$ and every s < t. We show that the map $u mapsto x_u$ is Lipschitz continuous when u ranges in the set of step functions whose total variations are uniformly bounded, where $x_u$ is the solution of the impulsive control system corresponding to u. We also define the generalized solution of the impulsive control system corresponding to a measurable control functin of bounded variation.