Устойчивость дифференциально-разностных систем с линейно возрастающим запаздыванием. I. Линейные управляемые системы

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Устойчивость дифференциально-разностных систем с линейно возрастающим запаздыванием. I. Линейные управляемые системы. / Ekimov, A. V.; Zhabko, A. P.; Yakovlev, P. V.

в: Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya, Том 16, № 3, 2020, стр. 316-325.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{9f1e4df98dce41d1812f99761b78f644,

title = "Устойчивость дифференциально-разностных систем с линейно возрастающим запаздыванием. I. Линейные управляемые системы",

abstract = "The article considers a controlled system of linear differential-difference equations with a linearly increasing delay. Sufficient conditions for the asymptotic stability of such systems are known; however, general conditions for the stabilizability of controlled systems and constructive algorithms for constructing stabilizing controls have not yet been obtained. For a linear differential-difference equation of delayed type with linearly increasing delay, the canonical Zubov transformation is applied and conditions for the stabilization of such systems by static control are derived. An algorithm for checking the conditions for the existence of a stabilizing control and for its constructing is formulated. New theorems on stability analysis of systems of linear differential-difference equations with linearly increasing delay are proven. The results obtained can be applied to the case of systems with several proportional delays.",

keywords = "Asymptotic evaluation system, Asymptotic stability, Linearly increasing time delay, Stabilizing control, System of linear differential-difference equations, system of linear differential-difference equations, linearly increasing time delay, asymptotic stability, stabilizing control, asymptotic evaluation system",

author = "Ekimov, {A. V.} and Zhabko, {A. P.} and Yakovlev, {P. V.}",

year = "2020",

doi = "10.21638/11701/SPBU10.2020.308",

language = "русский",

volume = "16",

pages = "316--325",

journal = " ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ",

issn = "1811-9905",

publisher = "Издательство Санкт-Петербургского университета",

number = "3",

}

RIS

TY - JOUR

T1 - Устойчивость дифференциально-разностных систем с линейно возрастающим запаздыванием. I. Линейные управляемые системы

AU - Ekimov, A. V.

AU - Zhabko, A. P.

AU - Yakovlev, P. V.

PY - 2020

Y1 - 2020

N2 - The article considers a controlled system of linear differential-difference equations with a linearly increasing delay. Sufficient conditions for the asymptotic stability of such systems are known; however, general conditions for the stabilizability of controlled systems and constructive algorithms for constructing stabilizing controls have not yet been obtained. For a linear differential-difference equation of delayed type with linearly increasing delay, the canonical Zubov transformation is applied and conditions for the stabilization of such systems by static control are derived. An algorithm for checking the conditions for the existence of a stabilizing control and for its constructing is formulated. New theorems on stability analysis of systems of linear differential-difference equations with linearly increasing delay are proven. The results obtained can be applied to the case of systems with several proportional delays.

AB - The article considers a controlled system of linear differential-difference equations with a linearly increasing delay. Sufficient conditions for the asymptotic stability of such systems are known; however, general conditions for the stabilizability of controlled systems and constructive algorithms for constructing stabilizing controls have not yet been obtained. For a linear differential-difference equation of delayed type with linearly increasing delay, the canonical Zubov transformation is applied and conditions for the stabilization of such systems by static control are derived. An algorithm for checking the conditions for the existence of a stabilizing control and for its constructing is formulated. New theorems on stability analysis of systems of linear differential-difference equations with linearly increasing delay are proven. The results obtained can be applied to the case of systems with several proportional delays.

KW - Asymptotic evaluation system

KW - Asymptotic stability

KW - Linearly increasing time delay

KW - Stabilizing control

KW - System of linear differential-difference equations

KW - system of linear differential-difference equations

KW - linearly increasing time delay

KW - asymptotic stability

KW - stabilizing control

KW - asymptotic evaluation system

UR - http://www.scopus.com/inward/record.url?scp=85097455164&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/16a8cfa0-0d25-3af6-a0b1-9b98b6dcd2fc/

U2 - 10.21638/11701/SPBU10.2020.308

DO - 10.21638/11701/SPBU10.2020.308

M3 - статья

AN - SCOPUS:85097455164

VL - 16

SP - 316

EP - 325

JO - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ

JF - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ

SN - 1811-9905

IS - 3

ER -

ID: 71945020