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.
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
\Bibitem{Kur01}
\by G.~A.~Kurina
\paper Invertibility of an Operator Appearing in the Control Theory for Linear Systems
\jour Mat. Zametki
\yr 2001
\vol 70
\issue 2
\pages 230--236
\mathnet{http://mi.mathnet.ru/mzm736}
\crossref{https://doi.org/10.4213/mzm736}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1882412}
\zmath{https://zbmath.org/?q=an:1045.93011}
\transl
\jour Math. Notes
\yr 2001
\vol 70
\issue 2
\pages 206--212
\crossref{https://doi.org/10.1023/A:1010254808822}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000171684100025}
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https://www.mathnet.ru/eng/mzm736
https://doi.org/10.4213/mzm736
https://www.mathnet.ru/eng/mzm/v70/i2/p230
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