Coinsidence of the Gelig-Leonov-Yakubovich, Filippov, and Aizerman-Pyatnitsky definitions

Authors

  • Maria A. Kiseleva St. Petersburg State University, Universitetskaya nab., 7-9, St. Petersburg, 199034, Russian Federation;
  • Nikolay V. Kuznetsov St. Petersburg State University, Universitetskaya nab., 7-9, St. Petersburg, 199034, Russian Federation; University Jyvaskyla, Seminarenkatu 15, Jyvaskyla, 40014, Finland

Abstract

This paper studies a class of systems with discontinuous right-hand side, which is widely used in applications. Discontinuous systems are closely related to the concept of “differential inclusion”, which was first introduced in the works of A.Marchaud and S. K. Zaremba. In the following work three different ways to define differential inclusions are be given: Filippov, Aizerman-Pyatnitsky and Gelig-Leonov - Yakubovich definitions. For the class of systems under study it is shown when these definitions coincide, and when they differ. Refs 19. Figs 2.

Keywords:

differential inclusion, discontinuous system, extended nonlinearity

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Published

2015-05-01

How to Cite

Kiseleva, M. A., & Kuznetsov, N. V. (2015). Coinsidence of the Gelig-Leonov-Yakubovich, Filippov, and Aizerman-Pyatnitsky definitions. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2(2), 182–189. Retrieved from https://math-mech-astr-journal.spbu.ru/article/view/11147

Issue

Vol. 2 No. 2 (2015)

Section

Mathematics

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.