Geodesic
Linearization of differential inclusions
Serdica Mathematical Journal, Tome 49 (2023) no. 1–3, pp. 187-204.

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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.
Keywords: tangential transversality, nonseparation result, Lagrange multiplier rule, 34A12, 46N10, 47J22 
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Bivas, Mira; Krastanov, Mikhail; Ribarska, Nadezhda. Linearization of  differential inclusions. Serdica Mathematical Journal, Tome 49 (2023) no. 1–3, pp. 187-204. http://geodesic.mathdoc.fr/item/SMJ2_2023_49_1_3_a9/