Differential Inclusions and Quasi-Lyapunov Functions

Authors

  • Martin Ivanov  Sofia University “St. Kliment Ohridski”, Bulgaria
  • Mikhail Krastanov Sofia University “St. Kliment Ohridski”, Bulgaria and Bulgarian Academy of Sciences
  • Nadezhda Ribarska Sofia University “St. Kliment Ohridski”, Bulgaria and Bulgarian Academy of Sciences

DOI:

https://doi.org/10.7546/CRABS.2025.12.02

Keywords:

differential inclusions with nonconvex right-hand side, existence of solutions, quasi-Lyapunov function, invariance, Fuller problem

Abstract

A sufficient condition for existence of a solution of a differential inclusion with a uniformly bounded right-hand side that has nonempty closed (possibly nonconvex) values is obtained. An Olech-type result is obtained as a corollary. An example, which originates from the Fuller problem from optimal control theory, is given to demonstrate the applicability of the main result.

Author Biographies

Martin Ivanov , Sofia University “St. Kliment Ohridski”, Bulgaria

Mailing Address:
Faculty of Mathematics and Informatics,
Sofia University “St. Kliment Ohridski”,
5 James Bourchier Blvd, 1164 Sofia, Bulgaria

E-mail: mdobrinov@fmi.uni-sofia.bg

Mikhail Krastanov, Sofia University “St. Kliment Ohridski”, Bulgaria and Bulgarian Academy of Sciences

Mailing Addresses:
Faculty of Mathematics and Informatics,
Sofia University “St. Kliment Ohridski”,
5 James Bourchier Blvd, 1164 Sofia, Bulgaria
and
Institute of Mathematics and Informatics,
Bulgarian Academy of Sciences,
Akad. G. Bonchev St, Bl. 8,
1113 Sofia, Bulgaria

E-mail: krastanov@fmi.uni-sofia.bg

Nadezhda Ribarska, Sofia University “St. Kliment Ohridski”, Bulgaria and Bulgarian Academy of Sciences

Mailing Addresses:
Faculty of Mathematics and Informatics,
Sofia University “St. Kliment Ohridski”,
5 James Bourchier Blvd, 1164 Sofia, Bulgaria
and
Institute of Mathematics and Informatics,
Bulgarian Academy of Sciences,
Akad. G. Bonchev St, Bl. 8,
1113 Sofia, Bulgaria

E-mail: ribarska@fmi.uni-sofia.bg

Downloads

Published

23-12-2025

How to Cite

[1]
M. Ivanov, M. Krastanov, and N. Ribarska, “Differential Inclusions and Quasi-Lyapunov Functions”, C. R. Acad. Bulg. Sci., vol. 78, no. 12, pp. 1756–1764, Dec. 2025.

Issue

Vol. 78 No. 12 (2025)

Section

Mathematics

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