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**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.

### MSC:

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 |

### Keywords:

fault detection; generalized \(H_2\) performance; Markovian jump systems; partly known transition probabilities; 2-D systems; residual generation system; linear matrix inequalities; well-known Roesser model; asymptotical stability; Bernoulli random binary distribution### References:

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