Quadratic Lyapunov theory for dynamic linear switched systems.

dc.contributor.advisorDavis, John M. (John Marcus), 1974-
dc.contributor.authorEisenbarth, Geoffrey B.
dc.contributor.departmentMathematics.en_US
dc.contributor.schoolsBaylor University. Dept. of Mathematics.en_US
dc.date.accessioned2014-01-28T15:17:03Z
dc.date.available2014-01-28T15:17:03Z
dc.date.copyright2013-12
dc.date.issued2014-01-28
dc.description.abstractIn this work, a special class of time-varying linear systems in the arbitrary time scale setting is examined by considering the qualitative properties of their solutions. Building on the work of J. DaCunha and A. Ramos, Lyapunov's Second (or Direct) Method is utilized to determine when the solutions to a given switched system are asymptotically stable. Three major classes of switched systems are analyzed which exhibit a convenient containment scheme so as to recover early results as special cases of later, more general results. The stability of switched systems under both arbitrary and particular switching is considered, in addition to design parameters of the time scale domain which also imply stability. A new approach to Lyapunov theory for time scales is then considered for switched systems which do not necessarily belong to any class of systems, contrasting and generalizing previous results. Finally, extensions of the contained theory are considered and a nontrivial generalization of a major result by D. Liberzon and A. Agrachev is investigated and conjectured.en_US
dc.description.degreePh.D.en_US
dc.identifier.urihttp://hdl.handle.net/2104/8899
dc.language.isoen_USen_US
dc.publisheren
dc.rightsBaylor University theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact librarywebmaster@baylor.edu for inquiries about permission.en_US
dc.rights.accessrightsWorldwide accessen_US
dc.subjectDynamic equations.en_US
dc.subjectSwitched systems.en_US
dc.subjectHybrid systems.en_US
dc.subjectTime scales.en_US
dc.titleQuadratic Lyapunov theory for dynamic linear switched systems.en_US
dc.typeThesisen_US

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