Research output: Contribution to journal › Article › peer-review
Устойчивость дифференциально-разностных систем с линейно возрастающим запаздыванием. I. Линейные управляемые системы. / Ekimov, A. V.; Zhabko, A. P.; Yakovlev, P. V.
In: Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya, Vol. 16, No. 3, 2020, p. 316-325.Research output: Contribution to journal › Article › peer-review
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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.
N1 - Publisher Copyright: © 2020 Saint Petersburg State University. All rights reserved. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.
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