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\(H_\infty \) estimation for discrete-time piecewise homogeneous Markov jump linear systems. (English) Zbl 1180.93100

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:

93E10 Estimation and detection in stochastic control theory
93C55 Discrete-time control/observation systems
60J75 Jump processes (MSC2010)
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