Step average linear differential inclusions of variable dimension
Journal Title: Дослідження в математиці і механіці - Year 2017, Vol 22, Issue 1
Abstract
The theory of differential inclusions began its development in the early thirties of the 20th century with the publication A. Marsh and S. Zaremba. However, the rapid development of this theory began with the 60s of the last century thanks to the work of T. Wazewski and A.F. Filippov, which justified its close relationship with the theory of optimal control and differential equations with discontinuous right-hand side. Mathematical justification of the averaging method for ordinary differential equations stems from the fundamental work of N.M. Krylov and N.N. Bogolyubov. In the 70s, V.A. Plotnikov was justified by the possibility of the application of various schemes of the averaging method for differential inclusions. In this article The possibility of the use of turn-averaging scheme in the study of linear differential inclusions with variable dimension.
Authors and Affiliations
O. Kichmarenko, A. V. Plotnikov
Keywords
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