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Matematicheskie Zametki, 2001, Volume 70, Issue 2, Pages 230–236
DOI: https://doi.org/10.4213/mzm736 (Mi mzm736) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Invertibility of an Operator Appearing in the Control Theory for Linear Systems

G. A. Kurina

Voronezh State Academy of Forestry Engineering
Full-text PDF (165 kB) Citations (10)
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DOI: https://doi.org/10.4213/mzm736
Abstract: We give sufficient conditions for the existence of a bounded inverse operator for a linear operator appearing in the theory of optimal control of linear systems in Hilbert space and having a matrix representation of the form
$$ \begin {pmatrix} F_1&0&F_2 \\F_3&-F_1^*&F_5 \\-F_5^*&F_2^*&-F_4 \end{pmatrix} , $$
, where $F3$, $F4$ are nonnegative self-adjoint operators. The invertibility of the operator under study is used to prove the unique solvability of a certain two-point boundary-value problem that arises from conditions for optimal control.
Received: 03.04.2000
English version:
Mathematical Notes, 2001, Volume 70, Issue 2, Pages 206–212
DOI: https://doi.org/10.1023/A:1010254808822
Bibliographic databases:
UDC: 517.983.24
Language: Russian
Citation: G. A. Kurina, “Invertibility of an Operator Appearing in the Control Theory for Linear Systems”, Mat. Zametki, 70:2 (2001), 230–236; Math. Notes, 70:2 (2001), 206–212
Citation in format AMSBIB
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\jour Math. Notes
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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