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**Fault detection for nonlinear networked control systems with Markov data transmission pattern.**
*(English)*
Zbl 1267.93180

Summary: This paper is concerned with the fault-detection problem of nonlinear multiple channels data transmission networked control systems (NCSs). Two irrelevant Markov chains are introduced to describe the data transmission characterization of nonlinear delayed NCSs with data loss in both from sensors to controller and from controller to actuators, and a nonlinear Markovian jump system model is established. Based on this novel model, employing a mode-dependent fault-detection filter as residual generator, a fault-detection filter design of nonlinear NCSs is formulated as a nonlinear \(H_\infty\)-filtering problem. Then an appropriate Lyapunov functional is chosen to derive the sufficient condition which satisfies the stochastic stability and prescribes the \(H_\infty\) attenuation level simultaneously. Especially, the desired mode-dependent fault-detection filters are constructed in terms of certain linear matrix inequalities (LMIs), and explicit parameters are characterized if these LMIs are feasible. The effectiveness of the proposed method is demonstrated by a simulation example.

### MSC:

93E15 | Stochastic stability in control theory |

93B36 | \(H^\infty\)-control |

93C55 | Discrete-time control/observation systems |

94C12 | Fault detection; testing in circuits and networks |

### Keywords:

fault detection; nonlinear networked control system; Markovian jump system; multiple channels data transmission
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\textit{Y. Zhang} et al., Circuits Syst. Signal Process. 31, No. 4, 1343--1358 (2012; Zbl 1267.93180)

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