Sur la résolution des équations de Lyapunov et Riccati

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dc.contributor.authorBEZAI ASSIA
dc.date.accessioned2025-01-15T08:00:58Z
dc.date.available2025-01-15T08:00:58Z
dc.date.issued2024
dc.description.abstractThe aim of this thesis is to study the solvability of the Lyapunov (AX-XB = C), the Sylvester (AX-Y B = C) and the Riccati (AX-XB + XDX = C ) operator equations in Hilbert spaces of infinite dimensions using generalized inverses. More precisely, we give new necessary and sufficient conditions for the solvability to the operator equations AX-XB = C and AX-Y B = C; where A and B are group invertible. In addition the general solutions to the equation AX-Y B = C; are derived in terms of the group inverse of A and B. As a consequence, new necessary and sufficient conditions for the solvability to the operator equation AY-BY = C; are derived. Next by application of the generalized Drazin inverse, we give a new method for solving Riccati and Lyapunov operator equations in Hilbert space. Results are applied to Riccati and Lyapunov operator differential equations.
dc.identifier.urihttps://dspace.univ-batna2.dz/handle/123456789/1833
dc.language.isoen
dc.titleSur la résolution des équations de Lyapunov et Riccati
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