Zero Forcing, Linear and Quantum Controllability for Systems Evolving on Networks

dc.contributor.author Burgarth, Daniel
dc.contributor.author D'Alessandro, Domenico
dc.contributor.author Hogben, Leslie
dc.contributor.author Hogben, Leslie
dc.contributor.author Severini, Simone
dc.contributor.author Young, Michael
dc.contributor.department Electrical and Computer Engineering
dc.contributor.department Mathematics
dc.date 2018-02-18T05:30:44.000
dc.date.accessioned 2020-06-30T06:00:48Z
dc.date.available 2020-06-30T06:00:48Z
dc.date.copyright Tue Jan 01 00:00:00 UTC 2013
dc.date.issued 2013-09-01
dc.description.abstract <p>We study the dynamics of systems on networks from a linear algebraic perspective. The control theoretic concept of controllability describes the set of states that can be reached for these systems. Our main result says that controllability in the quantum sense, expressed by the Lie algebra rank condition, and controllability in the sense of linear systems, expressed by the controllability matrix rank condition, are equivalent conditions. We also investigate how the graph theoretic concept of a zero forcing set impacts the controllability property; if a set of vertices is a zero forcing set, the associated dynamical system is controllable. These results open up the possibility of further exploiting the analogy between networks, linear control systems theory, and quantum systems Lie algebraic theory. This study is motivated by several quantum systems currently under study, including continuous quantum walks modeling transport phenomena.</p>
dc.description.comments <p>This is a manuscript of an article published as Burgarth, Daniel, Domenico D'Alessandro, Leslie Hogben, Simone Severini, and Michael Young. "Zero forcing, linear and quantum controllability for systems evolving on networks." <em>IEEE Transactions on Automatic Control</em> 58, no. 9 (2013): 2349-2354. DOI: <a href="http://dx.doi.org/10.1109/TAC.2013.2250075" target="_blank">10.1109/TAC.2013.2250075</a>. Posted with permission.</p>
dc.format.mimetype application/pdf
dc.identifier archive/lib.dr.iastate.edu/math_pubs/61/
dc.identifier.articleid 1069
dc.identifier.contextkey 9873379
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath math_pubs/61
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/54658
dc.language.iso en
dc.source.bitstream archive/lib.dr.iastate.edu/math_pubs/61/2013_Hogben_ZeroForcing.pdf|||Sat Jan 15 01:16:15 UTC 2022
dc.source.uri 10.1109/TAC.2013.2250075
dc.subject.disciplines Algebra
dc.subject.disciplines Dynamical Systems
dc.subject.keywords Control
dc.subject.keywords graph
dc.subject.keywords Lie algebra
dc.subject.keywords quantum system
dc.subject.keywords walk matrix
dc.subject.keywords zero forcing
dc.title Zero Forcing, Linear and Quantum Controllability for Systems Evolving on Networks
dc.type article
dc.type.genre article
dspace.entity.type Publication
relation.isAuthorOfPublication 0131698a-00df-41ad-8919-35fb630b282b
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relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48
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