In this thesis we consider linear multivariable frequency response systems with finite numbers of unstable poles but with no poles on the j(omega) - axis. We represent unstable systems by input-output mappings with restricted domains in / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / The effects of unstable perturbations in an open loop system K on the closed loop system (I + K)('-1) are studied. For this purpose the gap metric is introduced for measuring approximations to unstable systems. This metric is used to determine the sets of "allowable" uncertainties, i.e., those which do not destroy the stability of a feedback system, and which preserve a specified tolerance on the closed loop input-output behavior. / It is shown that the allowable sets of uncertainties consist of closed operators which are contained in spheres sufficiently small in the gap metric. Also, all metrics which separate allowable uncertainties from the others are shown to generate the same topology as the gap. / It is shown that all admissible approximations to a nominal frequency response system have domains with the same codimension, and therefore the same number of r.h.p. poles as the nominal system. / Various estimates of the gap between two unstable systems are obtained, and applied to examples.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.68559 |
| Date | January 1981 |
| Creators | El-Sakkary, Ahmed Kamal. |
| 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: 000128004, proquestno: AAINK51946, Theses scanned by UMI/ProQuest. |
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