Coincidence of the Gelig–Leonov–Yakubovich, Filippov, and Aizerman–Pyatnitskiy definitions

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Coincidence of the Gelig–Leonov–Yakubovich, Filippov, and Aizerman–Pyatnitskiy definitions. / Kiseleva, M. A.; Kuznetsov, N. V.

In: Vestnik St. Petersburg University: Mathematics, Vol. 48, No. 2, 09.04.2015, p. 66-71.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{16516fa2c6294d6a84333a82d4cfa526,

title = "Coincidence of the Gelig–Leonov–Yakubovich, Filippov, and Aizerman–Pyatnitskiy definitions",

abstract = "This paper investigates a class of systems with discontinuous right-hand side, which are widely used in applications. Discontinuous systems are closely related to the concept of differential inclusion, which was first introduced by A. Marchaud and S.K. Zaremba. Three different approaches to the definition of differential inclusions are presented: the Filippov, the Aizerman–Pyatnitskiy, and the Gelig–Leonov–Yakubovich definitions. For the class of systems considered, it is shown when these definitions coincide and when they are different.",

keywords = "differential inclusion, discontinuous system, extended nonlinearity",

author = "Kiseleva, {M. A.} and Kuznetsov, {N. V.}",

note = "Publisher Copyright: {\textcopyright} 2015, Allerton Press, Inc.",

year = "2015",

month = apr,

day = "9",

doi = "10.3103/S1063454115020041",

language = "English",

volume = "48",

pages = "66--71",

journal = "Vestnik St. Petersburg University: Mathematics",

issn = "1063-4541",

publisher = "Pleiades Publishing",

number = "2",

}

RIS

TY - JOUR

T1 - Coincidence of the Gelig–Leonov–Yakubovich, Filippov, and Aizerman–Pyatnitskiy definitions

AU - Kiseleva, M. A.

AU - Kuznetsov, N. V.

PY - 2015/4/9

Y1 - 2015/4/9

N2 - This paper investigates a class of systems with discontinuous right-hand side, which are widely used in applications. Discontinuous systems are closely related to the concept of differential inclusion, which was first introduced by A. Marchaud and S.K. Zaremba. Three different approaches to the definition of differential inclusions are presented: the Filippov, the Aizerman–Pyatnitskiy, and the Gelig–Leonov–Yakubovich definitions. For the class of systems considered, it is shown when these definitions coincide and when they are different.

AB - This paper investigates a class of systems with discontinuous right-hand side, which are widely used in applications. Discontinuous systems are closely related to the concept of differential inclusion, which was first introduced by A. Marchaud and S.K. Zaremba. Three different approaches to the definition of differential inclusions are presented: the Filippov, the Aizerman–Pyatnitskiy, and the Gelig–Leonov–Yakubovich definitions. For the class of systems considered, it is shown when these definitions coincide and when they are different.

KW - differential inclusion

KW - discontinuous system

KW - extended nonlinearity

UR - http://www.scopus.com/inward/record.url?scp=84930649997&partnerID=8YFLogxK

U2 - 10.3103/S1063454115020041

DO - 10.3103/S1063454115020041

M3 - Article

VL - 48

SP - 66

EP - 71

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 2

ER -

ID: 4004173