Geodesic
Invertibility of an Operator Appearing in the Control Theory for Linear Systems
Matematičeskie zametki, Tome 70 (2001) no. 2, pp. 230-236

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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 $$ \begin {pmatrix} F_10 \\F_3-F_1^* \\-F_5^*^*-F_4 \end{pmatrix} , $$ , 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. 
@article{MZM_2001_70_2_a6,
     author = {G. A. Kurina},
     title = {Invertibility of an {Operator} {Appearing} in the {Control} {Theory} for {Linear} {Systems}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {230--236},
     publisher = {mathdoc},
     volume = {70},
     number = {2},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_70_2_a6/}
}
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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/