Discrete-time linear periodically time-varying systems: Analysis, realization and model reduction

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dc.contributor.advisorAntoulas, Athanasios C.en_US
dc.creatorHu, Jingen_US
dc.date.accessioned2009-06-04T08:03:16Zen_US
dc.date.available2009-06-04T08:03:16Zen_US
dc.date.issued2003en_US
dc.description.abstractDiscrete-time linear periodically time-varying (LPTV) systems, considered as a bridge between the well-studied linear time-invariant (LTI) model and the nonlinear time-varying problems in real world, have been receiving increasing attention in recent a few decades. In this research project, we try to understand discrete-time LPTV systems both internally and externally and derive basic theories for analysis, realization and model reduction of LPTV systems. Firstly we review the system model for LPTV systems, define its transfer function matrix, Markov parameters, stability, reachability and observability. Then we emphasize on the numerically efficient and stable methods to compute LPTV system grammians and to approximate the eigenvalue decay rate. Another main result of this thesis is Krylov-based moment matching algorithm for model reduction of LPTV systems, which is derived afterwards, and is also compared to the other approach: balancing and balanced truncation of LPTV systems. Almost any application of discrete-time LPTV systems, including periodic digital filters and periodic control theories, demands a periodic state-space model from input-output maps. This periodic realization problem is treated at the end of the thesis with demonstration of applicable non-minimal and quasi-minimal realization methods.en_US
dc.format.extent86 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS E.E. 2004 HUen_US
dc.identifier.citationHu, Jing. "Discrete-time linear periodically time-varying systems: Analysis, realization and model reduction." (2003) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/17688">https://hdl.handle.net/1911/17688</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/17688en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectMathematicsen_US
dc.subjectElectronicsen_US
dc.subjectElectrical engineeringen_US
dc.titleDiscrete-time linear periodically time-varying systems: Analysis, realization and model reductionen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentElectrical Engineeringen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Scienceen_US
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