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The $$H_2$$-control for jump linear systems: Cluster observations of the Markov state. (English) Zbl 0991.93125
Summary: The $$H_2$$-norm control problem of discrete-time Markov jump linear system 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 recovers the situation of 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 M. C. de Oliveira J. Bernussou and J. C. Geromel [Syst. Control Lett. 37, 261-265 (1999; Zbl 0948.93058)] involving an LMI characterization to establish an $$H_2$$ 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.

##### MSC:
 93E20 Optimal stochastic control 60J75 Jump processes (MSC2010)
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##### References:
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