Controllability, Observability, Realizability, and Stability of Dynamic Linear Systems

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dc.creatorDavis, John M.
dc.creatorGravagne, Ian A.
dc.creatorJackson, Billy J.
dc.creatorMarks II, Robert J.
dc.date2009-01-23
dc.date2009-03-03
dc.date.accessioned2026-07-07T12:47:52Z
dc.date.available2026-07-07T12:47:52Z
dc.descriptionWe develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time domains. The approach here is based on generalized Laplace transform methods (e.g. shifts and convolution) from our recent work \cite{DaGrJaMaRa}. We study controllability in terms of the controllability Gramian and various rank conditions (including Kalman's) in both the time invariant and time varying settings and compare the results. We also explore observability in terms of both Gramian and rank conditions as well as realizability results. We conclude by applying this systems theory to connect exponential and BIBO stability problems in this general setting. Numerous examples are included to show the utility of these results.
dc.descriptiontypos corrected; current form is as accepted in EJDE
dc.identifierhttps://arxiv.org/abs/0901.3764
dc.identifierhttp://arxiv.org/abs/0901.3764
dc.identifierElectron. J. Diff. Eqns., Vol. 2009(2009), No. 37, pp. 1-32
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/221864
dc.subjectOptimization and Control
dc.subjectDynamical Systems
dc.subject93B05; 93B07; 93B20; 93B55; 93D99
dc.titleControllability, Observability, Realizability, and Stability of Dynamic Linear Systems
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