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Let $\dot{x}=f(x,u)$ 
be a general control system; the existence of asmooth control-Lyapunov function does not imply the existence of a continuousstabilizing feedback. However, we show that it allows us to design astabilizing feedback in the Krasovskii (or Filippov) sense. Moreover,we recall a definition of a control-Lyapunov functionin the case of a nonsmooth function; it is based on Clarke'sgeneralized gradient. Finally, with an inedite proof we prove that the existence of this type of control-Lyapunov function is equivalent to the existence of aclassical control-Lyapunov function. This property leads to a generalizationof a result on the systems with integrator.
