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Vol. 49 No. 1–3 (2023)
Serdica Mathematical Journal

Articles

Linearization of differential inclusions

https://doi.org/10.55630/serdica.2023.49.187-204

Published 20-11-2023

  • Mira Isak Bivas
    • ,
  • Mikhail Ivanov Krastanov
    • ,
  • Nadezhda Kostadinova Ribarska

Mira Isak Bivas
Sofia University, Faculty of Mathematics and Informatics and Institute of Mathematics and Informatics, Bulgarian Academy of Sciences

Mikhail Ivanov Krastanov
Sofia University, Faculty of Mathematics and Informatics and Institute of Matematics and Informatics, Bulgarian Academy of Sciences

Nadezhda Kostadinova Ribarska
Sofia University, Faculty of Mathematics and Informatics and Institute of Matematics and Informatics, Bulgarian Academy of Sciences

Abstract

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.

2020 Mathematics Subject Classification:

34A12, 46N10, 47J22

Keywords

tangential transversality, nonseparation result, Lagrange multiplier rule

Full text

Author Details

Mira Isak Bivas

Faculty of Mathematics and Informatics
Sofia University
5, James Bourchier Blvd
1126 Sofia, Bulgaria
mira.bivas@fmi.uni-sofia.bg
and
Institute of Mathematics and Informatics
Bulgarian Academy of Sciences
G. Bonchev Str., Bl. 8
1113 Sofia, Bulgaria

Mikhail Ivanov Krastanov

Faculty of Mathematics and Informatics
Sofia University
5, James Bourchier Blvd
1126 Sofia, Bulgaria
krastanov@fmi.uni-sofia.bg
and
Institute of Mathematics and Informatics
Bulgarian Academy of Sciences
G. Bonchev Str., Bl. 8
1113 Sofia, Bulgaria

Nadezhda Kostadinova Ribarska

Faculty of Mathematics and Informatics
Sofia University
5, James Bourchier Blvd
1126 Sofia, Bulgaria
ribarska@fmi.uni-sofia.bg
and
Institute of Mathematics and Informatics
Bulgarian Academy of Sciences
G. Bonchev Str., Bl. 8
1113 Sofia, Bulgaria

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