Geodesic
Invertibility of an Operator Appearing in the Control Theory for Linear Systems
Matematičeskie zametki, Tome 70 (2001) no. 2, pp. 230-236 
G. A. Kurina. Invertibility of an Operator Appearing in the Control Theory for Linear Systems. Matematičeskie zametki, Tome 70 (2001) no. 2, pp. 230-236. http://geodesic.mathdoc.fr/item/MZM_2001_70_2_a6/
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     author = {G. A. Kurina},
     title = {Invertibility of an {Operator} {Appearing} in the {Control} {Theory} for {Linear} {Systems}},
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     pages = {230--236},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_70_2_a6/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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