Generalized \(H_2\) fault detection for two-dimensional Markovian jump systems. (English) Zbl 1268.93096

Summary: This paper is concerned with the generalized \(H_{2}\) fault detection for two-dimensional (2-D) discrete-time Markovian jump systems. The mathematical model of the 2-D system is established upon the well-known Roesser model, and the measurement missing phenomenon, which appears typically in a network environment, is modeled by a stochastic variable satisfying the Bernoulli random binary distribution. In addition, the transition probabilities of the Markovian jump process are assumed to be partly accessed, that is, the transition probabilities are partly known. Our attention is focused on the design of a fault detection filter, or a residual generation system, which guarantees the fault detection system to be mean-square asymptotically stable and to have a prescribed generalized \(H_{2}\) performance. Sufficient conditions for the existence of a desired fault detection filter are established in terms of Linear Matrix Inequalities (LMIs). A numerical example is provided to illustrate the effectiveness of the proposed design method.


93C55 Discrete-time control/observation systems
93E03 Stochastic systems in control theory (general)
60J75 Jump processes (MSC2010)
94C12 Fault detection; testing in circuits and networks
93D20 Asymptotic stability in control theory
Full Text: DOI Link


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