Fault detection for nonlinear networked systems with random packet dropout and probabilistic interval delay.

*(English)*Zbl 1263.93211Summary: In this paper, the fault detection (FD) problem of nonlinear networked control systems (NCSs) is investigated. A nonlinear stochastic systems model is proposed to account for the NCSs with network-induced random packet dropout and non-uniformly distributed time-varying delay in both from sensor to controller and from controller to actuator. On the basis of the new model, by employing FD filter as residual generator, the addressed FD problem is converted into auxiliary nonlinear \(H_{\infty }\) filtering problem. Then, with the help of Lyapunov functional approach, a sufficient condition for the desired FD filter is constructed in terms of certain linear matrix inequalities, which depends on not only nonlinear level but also delay interval occurrence rate and successful joint packet transmission rate. Especially, a trade-off phenomenon among maximum allowable delay bound, nonlinear level, and successful joint packet transmission rate is found, which typically resulted from the limited bandwidth of the communication networks. The effectiveness of the proposed methods is demonstrated by simulation examples.

##### MSC:

93E03 | Stochastic systems in control theory (general) |

93B52 | Feedback control |

93E11 | Filtering in stochastic control theory |

93C55 | Discrete-time control/observation systems |

##### Keywords:

fault detection; nonlinear networked control systems; random packet dropout; non-uniformly distributed delay
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\textit{Y. Zhang} and \textit{H. Fang}, Int. J. Adapt. Control Signal Process. 25, No. 12, 1074--1086 (2011; Zbl 1263.93211)

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