Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/75969
Type: Artigo de periódico
Title: Weak detectability and the linear-quadratic control problem of discrete-time Markov jump linear systems
Author: Costa, EF
Do Val, JBR
Abstract: The paper deals with the stochastic concepts of weak detectability and weak observability for Markov jump linear systems, which is an special class of composite linear systems. The concepts are explored here to strengthen the similarities with the corresponding concepts of deterministic detectability and observability. We introduce a collection of matrices, referred to as the observability matrices. We show that weak observability is equivalent to full rank of each matrix in the set of observability matrices. In addition, we present a stochastic counterpart of the well known result on the invariance of trajectories within non-observable subspaces. These characterizations allow us to clarify the relationship between weak detectability and mean square detectability and to provide a testable condition for weak detectability. Relying on the assumption of weak detectability, we develop a method for solving the linear quadratic problem that is based on iterations of uncoupled algebraic Riccati equations, which converges to the solution of the coupled algebraic Riccati equation if and only if the system is mean-square stabilizable. Numerical examples are included.
Country: Inglaterra
Editor: Taylor & Francis Ltd
Rights: fechado
Identifier DOI: 10.1080/002071702000023717
Date Issue: 2002
Appears in Collections:Unicamp - Artigos e Outros Documentos

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