G-2007-73
Mode-dependent Filtering for Discrete-Time Markovian Jump Linear Systems with Partly Unknown Transition Probabilities
and BibTeX reference
In this paper, the problem of filtering for a class of
discrete-time Markovian jump linear systems (MJLS) with partly unknown
transition probabilities is investigated. The considered systems are more
general, which cover the MJLS with completely known and completely unknown
transition probabilities as two special cases. A mode-dependent full-order
filter is constructed and the bounded real lemma (BRL) for the resulting
filtering error system is derived via LMI formulation. Then, an improved
version of the BRL is further given by introducing additional slack matrix
variables to eliminate the cross coupling between system matrices and
Lyapunov matrices among different operation modes. Finally, the existence
criterion of the desired filter is obtained such that the corresponding
filtering error system is stochastically stable with a guaranteed
performance index. A numerical example is presented to illustrate the
effectiveness and potential of the developed theoretical results.
Published September 2007 , 20 pages
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