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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2016, Volume 22, Number 2, Pages 129–137
DOI: https://doi.org/10.21538/0134-4889-2016-22-2-129-137 (Mi timm1298) 		 
The Riccati equation for autonomous linear systems with unbounded aftereffect

Yu. F. Dolgiiab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
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DOI: https://doi.org/10.21538/0134-4889-2016-22-2-129-137
Abstract: The problem of optimal stabilization for autonomous linear systems of differential equations with unbounded aftereffect is considered. The reduction of the solvability problem for the Riccati operator equation to the analogous problem for the Riccati functional-differential equation is proved. A class of systems of differential equations with unbounded aftereffect for which the Riccati functional-differential equation can be solved analytically is described.
Keywords: differential equations with aftereffect, optimal stabilizing control, quadratic performance index, Riccati equation.
Received: 25.01.2016
Bibliographic databases:
Document Type: Article
UDC: 517.929
MSC: 34K06, 34K20, 34K30
Language: Russian
Citation: Yu. F. Dolgii, “The Riccati equation for autonomous linear systems with unbounded aftereffect”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 2, 2016, 129–137
Citation in format AMSBIB
\Bibitem{Dol16}
\by Yu.~F.~Dolgii
\paper The Riccati equation for autonomous linear systems with unbounded aftereffect
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2016
\vol 22
\issue 2
\pages 129--137
\mathnet{http://mi.mathnet.ru/timm1298}
\crossref{https://doi.org/10.21538/0134-4889-2016-22-2-129-137}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3559169}
\elib{https://elibrary.ru/item.asp?id=26040825}
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