Lyapunov Criterion for Stochastic Systems and Its Applications in Distributed Computation

dc.contributor.authorQin, Yuzhen
dc.contributor.authorCao, Ming
dc.contributor.authorAnderson, Brian
dc.date.accessioned2021-03-12T00:42:40Z
dc.date.issued2020
dc.date.updated2020-11-15T07:28:12Z
dc.description.abstractThis paper presents new sufficient conditions for convergence and asymptotic or exponential stability of a stochastic discrete-time system, under which the constructed Lyapunov function always decreases in expectation along the system's solutions after a finite number of steps, but without necessarily strict decrease at every step, in contrast to the classical stochastic Lyapunov theory. As the first application of this new Lyapunov criterion, we look at the product of any random sequence of stochastic matrices, including those with zero diagonal entries, and obtain sufficient conditions to ensure the product almost surely converges to a matrix with identical rows; we also show that the rate of convergence can be exponential under additional conditions. As the second application, we study a distributed network algorithm for solving linear algebraic equations. We relax existing conditions on the network structures, while still guaranteeing the equations are solved asymptotically.en_AU
dc.format.mimetypeapplication/pdfen_AU
dc.identifier.issn0018-9286en_AU
dc.identifier.urihttp://hdl.handle.net/1885/227135
dc.language.isoen_AUen_AU
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE Inc)en_AU
dc.rights© 2019 IEEEen_AU
dc.sourceIEEE Transactions on Automatic Controlen_AU
dc.subjectAgreementen_AU
dc.subjectdistributed algorithmsen_AU
dc.subjectproducts of stochastic matricesen_AU
dc.subjectStochastic Lyapunov functionsen_AU
dc.titleLyapunov Criterion for Stochastic Systems and Its Applications in Distributed Computationen_AU
dc.typeJournal articleen_AU
local.bibliographicCitation.issue2en_AU
local.bibliographicCitation.lastpage560en_AU
local.bibliographicCitation.startpage546en_AU
local.contributor.affiliationQin, Yuzhen, University of Groningenen_AU
local.contributor.affiliationCao, Ming, University of Groningenen_AU
local.contributor.affiliationAnderson, Brian, College of Engineering and Computer Science, ANUen_AU
local.contributor.authoremailu8104642@anu.edu.auen_AU
local.contributor.authoruidAnderson, Brian, u8104642en_AU
local.description.embargo2099-12-31
local.description.notesImported from ARIESen_AU
local.identifier.absfor080599 - Distributed Computing not elsewhere classifieden_AU
local.identifier.absseo970109 - Expanding Knowledge in Engineeringen_AU
local.identifier.ariespublicationu6269649xPUB610en_AU
local.identifier.citationvolume65en_AU
local.identifier.doi10.1109/TAC.2019.2910948en_AU
local.identifier.scopusID2-s2.0-85079818904
local.identifier.uidSubmittedByu6269649en_AU
local.publisher.urlhttps://www.ieee.org/en_AU
local.type.statusPublished Versionen_AU

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