In this study, we address the factorization problem in the Hardy H('p) spaces, and provide a fast algorithm for its implementation with applications to some important engineering problems. The Thesis is presented in three autonomous papers. / In the first paper we lay down the technical foundation of the new approach in the scalar case. First, the factorization problem is formulated in the H('p) spaces. A formulation with sufficient generality to encompass practically all such engineering problems. Necessary and sufficient conditions for the existence of the spectral factors are derived, and a characterization of the class of functions admitting a canonical factorization is obtained. The reduction method is applied to certain Toeplitz equations in H('2) space to generate a sequence of approximate spectral factors. When the Laguerre basis is used in the reduction method the Toeplitz equation turns out to a Toeplitz set of linear equations. We also provide an error bound and an estimate for the speed of convergence. / In the second paper the matrix version of all the scalar results is provided and enriched with discussions and extension. In particular, we have shown that the factorization problem is associated with the solutions of certain Toeplitz equations in / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / spaces. The classical Gohberg-Krein factorization is re-examined within the framework developed here, and the connections between the outer-factorization, the canonical factorization, and inversion of certain Toeplitz operators have also been unveiled. / In Part III we generalize the Davis and Barry formula for the feedback gain in the LQR problems. The new setting, equipped with the spectral factorization method, provides fast and efficient algorithms for solving a wide class of LQR problems, rational matrix factorization, and positive polynomials factorization. Our parallel results for the discrete time case are given in brief together with many interesting computational properties.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.68715 |
| Date | January 1981 |
| Creators | Ahmed, Moustafa Elshafei. |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Doctor of Philosophy (Department of Electrical Engineering) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 000139122, proquestno: AAINL10272, Theses scanned by UMI/ProQuest. |
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