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Zbl 1180.93100
Zhang, Lixian
$H_\infty$ estimation for discrete-time piecewise homogeneous Markov jump linear systems.
(English)
[J] Automatica 45, No. 11, 2570-2576 (2009). ISSN 0005-1098

Summary: This paper concerns the problem of $H_\infty$ estimation for a class of Markov Jump Linear Systems (MJLS) with time-varying Transition Probabilities (TPs) in discrete-time domain. The time-varying character of TPs is considered to be finite piecewise homogeneous and the variations in the finite set are considered to be of two types: arbitrary variation and stochastic variation, respectively. The latter means that the variation is subject to a higher-level transition probability matrix. The mode-dependent and variation-dependent $H_\infty$ filter is designed such that the resulting closed-loop systems are stochastically stable and have a guaranteed $H_\infty$ filtering error performance index. Using the idea in the recent studies of partially unknown TPs for the traditional MJLS with homogeneous TPs, a generalized framework covering the two kinds of variations is proposed. A numerical example is presented to illustrate the effectiveness and the potential of the developed theoretical results.
MSC 2000:
*93E10 Estimation and detection in stochastic control
93C55 Discrete-time control systems
60J75 Jump processes

Keywords: Markov jump linear systems; $H_\infty$ filtering; piecewise homogeneous TPs; arbitrary variation and stochastic variation of TP matrices

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