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

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dc.contributor.advisorAntoulas, Athanasios C.
dc.creatorHu, Jing
dc.date.accessioned2009-06-04T08:03:16Z
dc.date.available2009-06-04T08:03:16Z
dc.date.issued2003
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.
dc.format.extent86 p.en_US
dc.format.mimetypeapplication/pdf
dc.identifier.callnoTHESIS E.E. 2004 HU
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>.
dc.identifier.urihttps://hdl.handle.net/1911/17688
dc.language.isoeng
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.
dc.subjectMathematics
dc.subjectElectronics
dc.subjectElectrical engineering
dc.titleDiscrete-time linear periodically time-varying systems: Analysis, realization and model reduction
dc.typeThesis
dc.type.materialText
thesis.degree.departmentElectrical Engineering
thesis.degree.disciplineEngineering
thesis.degree.grantorRice University
thesis.degree.levelMasters
thesis.degree.nameMaster of Science
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