Fault detection for uncertain switched systems with time-varying delays.

*(English)*Zbl 1395.93163Summary: This paper focuses on the fault detection (FD) problem for a class of uncertain switched systems with time-varying delays. The FD framework consists of the fault detection filters (FDFs) and a switching law. The resulting FDFs are with varying gains, which are expressed in the form of a linear parameter-varying (LPV) switched system. In special case, the proposed FDFs can be converted into the existing ones with fixed gains. The switching law satisfies the mode-dependent average dwell time (MDADT), which guarantees that each subsystem of the overall switched system is allowed to have its own average dwell time (ADT). Thus, the proposed design method leads to less conservatism and provides more flexibility. Delay-dependent conditions for the existence of the FDFs associated with the corresponding MDADT switching are formulated in terms of a set of linear matrix inequalities (LMIs), which ensure the exponential stability as well as a prescribed weighted \(L_2\)-gain for the errors between the residuals and faults. Two examples are given to illustrate the effectiveness of the theoretical results.

##### MSC:

93B12 | Variable structure systems |

93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |

93E11 | Filtering in stochastic control theory |

93C41 | Control/observation systems with incomplete information |

93C05 | Linear systems in control theory |

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\textit{G.-X. Zhong} and \textit{G.-H. Yang}, J. Franklin Inst. 352, No. 4, 1455--1475 (2015; Zbl 1395.93163)

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