Sur la résolution des équations de Lyapunov et Riccati
| dc.contributor.author | BEZAI ASSIA | |
| dc.date.accessioned | 2024-05-14T09:08:03Z | |
| dc.date.available | 2024-05-14T09:08:03Z | |
| dc.date.issued | 2024 | |
| dc.description.abstract | The aim of this thesis is to study the solvability of the Lyapunov (AXXB = 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. Key words : Hilbert spaces, Inner inverse, Drazin inverse, Group inverse, Generalized Drazin inverse, Lyapunov equation, Riccati equation, Sylvester equation, Pseudo-similarity, Pseudo-equivalence. AMS Classification : Primary 47A62; Secondary 15A09. | |
| dc.identifier.uri | https://dspace.univ-batna2.dz/handle/123456789/1742 | |
| dc.language.iso | fr | |
| dc.title | Sur la résolution des équations de Lyapunov et Riccati |