Structured noncommutative multidimensional linear systems

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dc.contributorVirginia Techen
dc.contributor.authorBall, Joseph A.en
dc.contributor.authorGroenewald, Gilberten
dc.contributor.authorMalakorn, Taniten
dc.contributor.departmentMathematicsen
dc.date.accessed2014-05-27en
dc.date.accessioned2014-05-28T18:35:02Zen
dc.date.available2014-05-28T18:35:02Zen
dc.date.issued2005en
dc.description.abstractWe introduce a class of multidimensional linear systems with evolution along a free semigroup. The transfer function for such a system is a formal power series in noncommuting indeterminates. Standard system-theoretic properties ( the operations of cascade/parallel connection and inversion, controllability, observability, Kalman decomposition, state-space similarity theorem, minimal state-space realizations, Hankel operators, realization theory) are developed for this class of systems. We also draw out the connections with the much earlier studied theory of rational and recognizable formal power series. Applications include linear-fractional models for classical discrete-time systems with structured, time-varying uncertainty, dimensionless formulas in robust control, multiscale systems and automata theory, and the theory of formal languages.en
dc.description.sponsorship.S. National Science Foundation under grant DMS-9987636en
dc.description.sponsorshipational Research Foundation of South Africa under grant 2053733en
dc.description.sponsorshipNaresuan University, Thailanden
dc.identifier.citationBall, J. A.; Groenewald, G.; Malakorn, T., "Structured noncommutative multidimensional linear systems," SIAM J. Control Optim., 44(4), 1474-1528, (2005). DOI: 10.1137/s0363012904443750en
dc.identifier.doihttps://doi.org/10.1137/s0363012904443750en
dc.identifier.issn0363-0129en
dc.identifier.urihttp://hdl.handle.net/10919/48136en
dc.identifier.urlhttp://epubs.siam.org/doi/abs/10.1137/S0363012904443750en
dc.language.isoen_USen
dc.publisherSiam Publicationsen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectmultidimensional linear systemsen
dc.subjectfree semigroupen
dc.subjectcontrollabilityen
dc.subjectobservabilityen
dc.subjectminimalityen
dc.subjectrealizationen
dc.subjectformal power seriesen
dc.subjectnoncommuting indeterminatesen
dc.subjectuncertain systemsen
dc.subjectiterative circuitsen
dc.subjectrealization-theoryen
dc.subjectc-nen
dc.subjectdiscreteen
dc.subjectrepresentationsen
dc.subjectminimalityen
dc.subjectdomainsen
dc.subjectmodelsen
dc.subjectseriesen
dc.subjectautomation & control systemsen
dc.subjectmathematics, applieden
dc.titleStructured noncommutative multidimensional linear systemsen
dc.title.serialSiam Journal on Control and Optimizationen
dc.typeArticleen

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