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Avtomatika i Telemekhanika, 2000, Issue 7, Pages 15–31 (Mi at312)  
This article is cited in 10 scientific papers (total in 10 papers)

Deterministic Systems

A linear-quadratic problem for systems with delay in the state. Exact solutions of Riccati equations

A. V. Kim, A. B. Lozhnikov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
Full-text PDF (248 kB) Citations (10)
Presented by the member of Editorial Board: V. B. Kolmanovskii

Received: 22.11.1999
Bibliographic databases:
Document Type: Article
UDC: 519.710
MSC: Primary 49K25; Secondary 49N10, 49N35
Language: Russian
Citation: A. V. Kim, A. B. Lozhnikov, “A linear-quadratic problem for systems with delay in the state. Exact solutions of Riccati equations”, Avtomat. i Telemekh., 2000, no. 7, 15–31; Autom. Remote Control, 61:7 (2000), 1076–1090
Citation in format AMSBIB
\Bibitem{KimLoz00}
\by A.~V.~Kim, A.~B.~Lozhnikov
\paper A~linear-quadratic problem for systems with delay in the state. Exact solutions of Riccati equations
\jour Avtomat. i Telemekh.
\yr 2000
\issue 7
\pages 15--31
\mathnet{http://mi.mathnet.ru/at312}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1805804}
\zmath{https://zbmath.org/?q=an:1063.49503}
\transl
\jour Autom. Remote Control
\yr 2000
\vol 61
\issue 7
\pages 1076--1090
Linking options:
  • https://www.mathnet.ru/eng/at312
  • https://www.mathnet.ru/eng/at/y2000/i7/p15
    • This publication is cited in the following 10 articles:
    1. B. G. Grebenschikov, A. B. Lozhnikov, “Metody issledovaniya ustoichivosti i stabilizatsii nekotorykh sistem s bolshim zapazdyvaniem”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 15:4 (2022), 99–108  mathnet  crossref
    2. Ortega-Martinez J.-M., Santos-Sanchez O.-J., Mondie S., “Comments on the Bellman Functional For Linear Time-Delay Systems”, Optim. Control Appl. Methods, 42:5 (2021), 1531–1540  crossref  isi
    3. Ortega-Martinez J., Santos-Sanchez O., Mondie S., “Lyapunov-Krasovskii Prescribed Derivative and the Bellman Functional For Time-Delay Systems”, IFAC PAPERSONLINE, 53:2 (2020), 7160–7165  crossref  isi
    4. Yu. F. Dolgii, “Tochnye resheniya zadachi optimalnoi stabilizatsii dlya sistem differentsialnykh uravnenii s posledeistviem”, Tr. IMM UrO RAN, 21, no. 4, 2015, 124–135  mathnet  mathscinet  elib
    5. Yu. F. Dolgii, “Lineino-kvadratichnaya zadacha upravleniya dlya sistem differentsialnykh uravnenii s posledeistviem”, Tr. IMM UrO RAN, 20, no. 3, 2014, 86–97  mathnet  mathscinet  elib
    6. N. I. Zhelonkina, A. B. Lozhnikov, A. N. Sesekin, “On pulse optimal control of linear systems with aftereffect”, Autom. Remote Control, 74:11 (2013), 1802–1809  mathnet  crossref  isi
    7. S. I. Solodushkin, “Stabilizatsiya lineinykh sistem s zapazdyvaniem po vremeni v koordinatakh i upravlenii”, Tr. IMM UrO RAN, 14, no. 4, 2008, 143–158  mathnet  elib
    8. Yu. F. Dolgii, “Stabilization of linear autonomous systems of differential equations with distributed delay”, Autom. Remote Control, 68:10 (2007), 1813–1825  mathnet  crossref  mathscinet  zmath
    9. A. N. Kotel'nikova, N. N. Krasovskii, “On correctness of probabilistic stabilization”, Autom. Remote Control, 68:10 (2007), 1826–1843  mathnet  crossref  mathscinet  zmath  elib  elib
    10. A. V. Kim, S. S. Rubleva, Y.-S. Choi, “On the problem of analytical construction of regulators for systems with delays”, Proc. Steklov Inst. Math. (Suppl.), 2005no. , suppl. 1, S122–S133  mathnet  mathscinet  zmath  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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