Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/74505
Type: Artigo de periódico
Title: Stabilizability and positiveness of solutions of the jump linear quadratic problem and the coupled algebraic Riccati equation
Author: do Val, JBR
Costa, EF
Abstract: This 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.
Subject: detectability
Markov jump linear systems (MJLSs)
observability
quadratic control problem
Country: EUA
Editor: Ieee-inst Electrical Electronics Engineers Inc
Rights: fechado
Identifier DOI: 10.1109/TAC.2005.846600
Date Issue: 2005
Appears in Collections:Artigos e Materiais de Revistas Científicas - Unicamp

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