Linearization of differential inclusions

In this paper we extend the approach of Dubovickiĭ and Miljutin for linearization of the dynamics of smooth control systems to a non-smooth setting. We consider dynamics governed by a differential inclusion and we study the Clarke tangent cone to the set of all admissible trajectories starting from a fixed point. Our approach is based on the classical Filippov’s theorem and on the important property “subtransversality” of two closed sets.