THE THEOREM OF BOHL–PERRON ON THE ASIMPTOTIC STABILITY OF HYBRID SYSTEMS AND INVERSE THEOREM-Reference-Cited by-同舟云学术

THE THEOREM OF BOHL–PERRON ON THE ASIMPTOTIC STABILITY OF HYBRID SYSTEMS AND INVERSE THEOREM

Published:2018 Issue:124 Volume: Page:726-737
ISSN:1810-0198
Container-title:Tambov University Reports. Series: Natural and Technical Sciences
language:
Short-container-title:Tamb. Un. Rep. Ser. Nat. Tech. Sci.

Author:

Simonov Pyotr Mikhailovich¹

Affiliation:

1. Perm State National Research University

Abstract

We consider an abstract hybrid system of two equations with two unknowns: a vector function x that is absolutely continuous on each finite interval [0,T], T>0, and a sequence of numerical vectors y. The study uses the W-method N.V. Azbelev. As a model, a system containing a functional differential equation with respect to x is used, and a difference equation with respect to y. Solutions spaces are studied. For a hybrid system, the Bohl–Perron theorem on asymptotic stability and the converse theorem are obtained.

Funder

Russian Foundation for Basic Research

Publisher

Tambov State University - G.R. Derzhavin

Reference27 articles.

1. Marchenko V.M, Luazo J.J. Ob ustoychivosti gibridnykh differentsial’no-raznostnykh sistem [On the stability of hybrid difference-differential systems]. Differentsial’nye uravneniya – Differential Equations, 2009, vol. 45, no. 5, pp. 728-740. (In Russian).

2. Simonov P.M. Teorema Bolya–Perrona dlya gibridnykh lineynykh sistem s posledeystviyem [Theorem of Bohl–Perron of hybrid linear functional differential systems with aftereffect]. Vestnik Permskogo universiteta. Seriya: Matematika. Mekhanika. Informatika – Bulletin of Perm University. Mathematics. Mechanics. Computer Science, 2016, no. 2 (33), pp. 56-60. (In Russian).

3. Simonov P.M. K voprosu o teoreme Bolya–Perrona dlya gibridnykh lineynykh funktsional’nodifferentsial’nykh sistem s posledeystviyem (GLFDSP) [On the question of the theorem of Bohl–Perron of hybrid linear functional differential systems with aftereffect (HLFDSA)]. Zhurnal Srednevolzhskogo matematicheskogo obshchestva – Middle Volga Mathematical Society Journal, 2016, vol. 18, no. 1, pp. 75-81. (In Russian).

4. Simonov P.M. Teorema Bolya–Perrona dlya gibridnykh lineynykh sistem s posledeystviyem [The Bohl–Perron theorem for hybrid linear systems with aftereffect]. Itogi nauki i tekhniki. Sovremennaya matematika i eye prilozheniya. Tematicheskiye obzory – Journal of Mathematical Sciences, 2017, vol. 132, pp. 122-126. (In Russian).

5. Simonov P.M. The Bohl–Perron theorem for hybrid linear systems with aftereffect. Journal of Mathematical Sciences, 2018, vol. 230, no. 5, pp. 775-781.