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Article: Positive operator based iterative algorithms for solving Lyapunov equations for Itô stochastic systems with Markovian jumps
Title | Positive operator based iterative algorithms for solving Lyapunov equations for Itô stochastic systems with Markovian jumps | ||||||||||||||
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Authors | |||||||||||||||
Keywords | Iteration Jump System Lyapunov Equation Markov Process Mean Square Stability Positive Operator Stochastic System | ||||||||||||||
Issue Date | 2011 | ||||||||||||||
Publisher | Elsevier Inc. The Journal's web site is located at http://www.elsevier.com/locate/amc | ||||||||||||||
Citation | Applied Mathematics And Computation, 2011, v. 217 n. 21, p. 8179-8195 How to Cite? | ||||||||||||||
Abstract | This paper studies the iterative solutions of Lyapunov matrix equations associated with Itô stochastic systems having Markovian jump parameters. For the discrete-time case, when the associated stochastic system is mean square stable, two iterative algorithms with one in direct form and the other one in implicit form are established. The convergence of the implicit iteration is proved by the properties of some positive operators associated with the stochastic system. For the continuous-time case, a transformation is first performed so that it is transformed into an equivalent discrete-time Lyapunov equation. Then the iterative solution can be obtained by applying the iterative algorithm developed for discrete-time Lyapunov equation. Similar to the discrete-time case, an implicit iteration is also proposed for the continuous case. For both discrete-time and continuous-time Lyapunov equations, the convergence rates of the established algorithms are analyzed and compared. Numerical examples are worked out to validate the effectiveness of the proposed algorithms. © 2011 Elsevier Inc. All rights reserved. | ||||||||||||||
Persistent Identifier | http://hdl.handle.net/10722/157115 | ||||||||||||||
ISSN | 2023 Impact Factor: 3.5 2023 SCImago Journal Rankings: 1.026 | ||||||||||||||
ISI Accession Number ID |
Funding Information: This work is supported in part by the National Natural Science Foundation of China under grant numbers 60904007, 61074111 and 10771044, the China Postdoctoral Science Foundation under grant number 20100480059, the Foundation for Innovative Research Group of the National Natural Science Foundation of China under grant 601021002, the Development Program for Outstanding Young Teachers at Harbin Institute of Technology under grant number HITQNJS.2009.054, the Heilongjiang Postdoctoral Foundation of China under Grant No. LRB10-194, HKU CRCG 201007176243, and by GRE HKU 7138/10E. | ||||||||||||||
References |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Li, ZY | en_US |
dc.contributor.author | Zhou, B | en_US |
dc.contributor.author | Lam, J | en_US |
dc.contributor.author | Wang, Y | en_US |
dc.date.accessioned | 2012-08-08T08:45:24Z | - |
dc.date.available | 2012-08-08T08:45:24Z | - |
dc.date.issued | 2011 | en_US |
dc.identifier.citation | Applied Mathematics And Computation, 2011, v. 217 n. 21, p. 8179-8195 | en_US |
dc.identifier.issn | 0096-3003 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/157115 | - |
dc.description.abstract | This paper studies the iterative solutions of Lyapunov matrix equations associated with Itô stochastic systems having Markovian jump parameters. For the discrete-time case, when the associated stochastic system is mean square stable, two iterative algorithms with one in direct form and the other one in implicit form are established. The convergence of the implicit iteration is proved by the properties of some positive operators associated with the stochastic system. For the continuous-time case, a transformation is first performed so that it is transformed into an equivalent discrete-time Lyapunov equation. Then the iterative solution can be obtained by applying the iterative algorithm developed for discrete-time Lyapunov equation. Similar to the discrete-time case, an implicit iteration is also proposed for the continuous case. For both discrete-time and continuous-time Lyapunov equations, the convergence rates of the established algorithms are analyzed and compared. Numerical examples are worked out to validate the effectiveness of the proposed algorithms. © 2011 Elsevier Inc. All rights reserved. | en_US |
dc.language | eng | en_US |
dc.publisher | Elsevier Inc. The Journal's web site is located at http://www.elsevier.com/locate/amc | en_US |
dc.relation.ispartof | Applied Mathematics and Computation | en_US |
dc.subject | Iteration | en_US |
dc.subject | Jump System | en_US |
dc.subject | Lyapunov Equation | en_US |
dc.subject | Markov Process | en_US |
dc.subject | Mean Square Stability | en_US |
dc.subject | Positive Operator | en_US |
dc.subject | Stochastic System | en_US |
dc.title | Positive operator based iterative algorithms for solving Lyapunov equations for Itô stochastic systems with Markovian jumps | en_US |
dc.type | Article | en_US |
dc.identifier.email | Lam, J:james.lam@hku.hk | en_US |
dc.identifier.authority | Lam, J=rp00133 | en_US |
dc.description.nature | link_to_subscribed_fulltext | en_US |
dc.identifier.doi | 10.1016/j.amc.2011.01.031 | en_US |
dc.identifier.scopus | eid_2-s2.0-79956076188 | en_US |
dc.identifier.hkuros | 208784 | - |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-79956076188&selection=ref&src=s&origin=recordpage | en_US |
dc.identifier.volume | 217 | en_US |
dc.identifier.issue | 21 | en_US |
dc.identifier.spage | 8179 | en_US |
dc.identifier.epage | 8195 | en_US |
dc.identifier.isi | WOS:000290622200004 | - |
dc.publisher.place | United States | en_US |
dc.identifier.scopusauthorid | Li, ZY=35240185200 | en_US |
dc.identifier.scopusauthorid | Zhou, B=7401906664 | en_US |
dc.identifier.scopusauthorid | Lam, J=7201973414 | en_US |
dc.identifier.scopusauthorid | Wang, Y=35294070900 | en_US |
dc.identifier.citeulike | 8960256 | - |
dc.identifier.issnl | 0096-3003 | - |