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dc.contributorVirginia Tech
dc.contributor.authorBall, Joseph A.
dc.contributor.authorGroenewald, Gilbert
dc.contributor.authorMalakorn, Tanit
dc.date.accessioned2014-05-28T18:35:02Z
dc.date.available2014-05-28T18:35:02Z
dc.date.issued2005
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/s0363012904443750
dc.identifier.issn0363-0129
dc.identifier.urihttp://hdl.handle.net/10919/48136
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.
dc.description.sponsorship.S. National Science Foundation under grant DMS-9987636
dc.description.sponsorshipational Research Foundation of South Africa under grant 2053733
dc.description.sponsorshipNaresuan University, Thailand
dc.language.isoen_US
dc.publisherSiam Publications
dc.subjectmultidimensional linear systems
dc.subjectfree semigroup
dc.subjectcontrollability
dc.subjectobservability
dc.subjectminimality
dc.subjectrealization
dc.subjectformal power series
dc.subjectnoncommuting indeterminates
dc.subjectuncertain systems
dc.subjectiterative circuits
dc.subjectrealization-theory
dc.subjectc-n
dc.subjectdiscrete
dc.subjectrepresentations
dc.subjectminimality
dc.subjectdomains
dc.subjectmodels
dc.subjectseries
dc.subjectautomation & control systems
dc.subjectmathematics, applied
dc.titleStructured noncommutative multidimensional linear systems
dc.typeArticle
dc.identifier.urlhttp://epubs.siam.org/doi/abs/10.1137/S0363012904443750
dc.date.accessed2014-05-27
dc.title.serialSiam Journal on Control and Optimization
dc.identifier.doihttps://doi.org/10.1137/s0363012904443750


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