Stabilizability and positiveness of solutions of the jump linear quadratic problem and the coupled algebraic Riccati equation

dc.creatordo Val, JBR
dc.creatorCosta, EF
dc.date2005
dc.dateMAY
dc.date2014-11-14T05:51:38Z
dc.date2015-11-26T17:13:33Z
dc.date2014-11-14T05:51:38Z
dc.date2015-11-26T17:13:33Z
dc.date.accessioned2018-03-29T00:01:54Z
dc.date.available2018-03-29T00:01:54Z
dc.identifierIeee Transactions On Automatic Control. Ieee-inst Electrical Electronics Engineers Inc, v. 50, n. 5, n. 691, n. 695, 2005.
dc.identifier0018-9286
dc.identifierWOS:000229085100017
dc.identifier10.1109/TAC.2005.846600
dc.identifierhttp://www.repositorio.unicamp.br/jspui/handle/REPOSIP/74505
dc.identifierhttp://www.repositorio.unicamp.br/handle/REPOSIP/74505
dc.identifierhttp://repositorio.unicamp.br/jspui/handle/REPOSIP/74505
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/1281597
dc.descriptionThis note addresses the jump linear quadratic problem of Markov jump linear systems and the associated algebraic Riccati equation. Necessary and sufficient conditions for stability of the optimal control and positiveness of Riccati solutions are developed. We show that the concept of weak detectability is not only a sufficient condition for the finiteness of cost functional to imply stablity of the associated trajectory, but also a necessary one. This, together with a characterization developed here for the kernel of the Riccati solution, allows us to show that the control solution stabilizes the system if and only if the system is weakly detectable, and that the Riccati solution is positive-definite if and only if the system is weakly observable. The connection between the algebraic Riccati equation and the control problem is made, as far as the minimal positive-semidefinite solution for the algebraic Riccati equation is identified with the optimal solution of the linear quadratic problem. Illustrative numerical examples and comparisons are included.
dc.description50
dc.description5
dc.description691
dc.description695
dc.languageen
dc.publisherIeee-inst Electrical Electronics Engineers Inc
dc.publisherPiscataway
dc.publisherEUA
dc.relationIeee Transactions On Automatic Control
dc.relationIEEE Trans. Autom. Control
dc.rightsfechado
dc.rightshttp://www.ieee.org/publications_standards/publications/rights/rights_policies.html
dc.sourceWeb of Science
dc.subjectdetectability
dc.subjectMarkov jump linear systems (MJLSs)
dc.subjectobservability
dc.subjectquadratic control problem
dc.subjectContinuous-time
dc.subjectDetectability Concept
dc.subjectStability Properties
dc.subjectWeak Detectability
dc.subjectGaussian Control
dc.subjectSystems
dc.subjectObservability
dc.titleStabilizability and positiveness of solutions of the jump linear quadratic problem and the coupled algebraic Riccati equation
dc.typeArtículos de revistas


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