The H2-control for jump linear systems: cluster observations of the Markov state

The H 2-norm control problem of discrete-time Markov jump linear systems is addressed in this paper when part of, or the total of the Markov states is not accessible to the controller. The non-observed part of the Markov states is grouped in a number of clusters of observations; the case with a sing...

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Bibliographic Details
Published in:Automatica (Oxford) 2002-02, Vol.38 (2), p.343-349
Main Authors: do Val, Joãao B.R., Geromel, Josè C., Gonçalves, Alim P.C.
Format: Article
Language:English
Subjects:
Applied sciences
Computer science
control theory
systems
Control system synthesis
Control theory. Systems
Exact sciences and technology
H2 control
Incomplete data
Markov models
Miscellaneous
Optimal control
Stabilizing feedback
Stochastic jump processes
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Summary:The H 2-norm control problem of discrete-time Markov jump linear systems is addressed in this paper when part of, or the total of the Markov states is not accessible to the controller. The non-observed part of the Markov states is grouped in a number of clusters of observations; the case with a single cluster retrieves the situation when no Markov state is observed. The control action is provided in linear feedback form, which is invariant on each cluster, and this restricted complexity setting is adopted, aiming at computable solutions. We explore a recent result by de Oliveira, Bernussou, and Geromel (Systems Control Lett. 37 (1999) 261) involving an LMI characterization to establish a H 2 solution that is stabilizing in the mean square sense. The novelty of the method is that it can handle in LMI form the situation ranging from no Markov state observation to complete state observation. In addition, when the state observation is complete, the optimal H 2-norm solution is retrieved.
ISSN:0005-1098
1873-2836
DOI:10.1016/S0005-1098(01)00210-2