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Fault detection of Markov jumping linear systems. (English) Zbl 1264.93246

Summary: The fault detection (FD) problems of discrete-time Markov jumping linear systems (MJLSs) are studied. We first focus on the stationary MJLS. The proposed FD system consists of two steps: residual generation and residual evaluation. A new reference model strategy is applied to construct a residual generator, such that it is robust against disturbances and sensitive to system faults. The generated residual signals are then evaluated according to their stochastic properties, and a threshold is computed for detecting the occurrences of faults. The upper bound of the corresponding false alarm rate (FAR) is also given. For the nonstationary MJLS, similar results are also obtained. All the solutions are presented in the form of linear matrix inequalities (LMIs). Finally, a numerical example is used to illustrate the results.

MSC:

93E11 Filtering in stochastic control theory
94C12 Fault detection; testing in circuits and networks
93B36 \(H^\infty\)-control
62M02 Markov processes: hypothesis testing
93C55 Discrete-time control/observation systems
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