Fault detection via factorization approach.

*(English)*Zbl 0703.93068Summary: Problems of designing fault detection and identification filters in the frequency domain are formulated and solved. Using the factorization approach a characterization of all fault detection filters is derived. This enables the derivation of necessary and sufficient conditions for the existence of fault identification as well as detection and isolation filters. It is shown that these conditions are a generalization of existing results of Y. Park and J. L. Stein [Int. J. Control 48, No.3, 1121–1136 (1988; Zbl 0659.93007)]. The formulas of constructing the filters are also derived. In comparison with the algorithms given in previous work they are computationally straightforward and simple. Finally, the proposed method for designing fault identification filters is extended so that more practical cases can be handled.

##### MSC:

93E10 | Estimation and detection in stochastic control theory |

93E11 | Filtering in stochastic control theory |

93E12 | Identification in stochastic control theory |

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

##### Keywords:

observer design; fault detection; identification filters; factorization approach; fault detection filters
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\textit{X. Ding} and \textit{P. M. Frank}, Syst. Control Lett. 14, No. 5, 431--436 (1990; Zbl 0703.93068)

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##### References:

[1] | Beard, R.V., Failure accomodation in linear systems through self-reorganization, () |

[2] | X. Ding and P.M. Frank, Detection of component failures via robust detection filters based on sensitivity analysis, Automatisierungstechnik (to appear). |

[3] | Francis, B.A., A course in \(H∞\) control theory, (1987), Springer-Verlag Berlin-New York |

[4] | Frank, P.M., Fault diagnosis in dynamic systems via state estimation - A survey, () |

[5] | Frank, P.M.; Wünnenberg, J., Evaluation of analytical redundancy for fault diagnosis using unknown input observer schemes, () |

[6] | Jones, H.L., Failure detection in linear systems, () |

[7] | Kailath, T., Linear systems, (1980), Prentice Hall Englewood Cliffs, NJ · Zbl 0458.93025 |

[8] | Massoumnia, M., A geometric approach to the synthesis of failure detection filters, IEEE trans. automat. control, 31, 839-846, (1986) · Zbl 0599.93017 |

[9] | Massoumnia, M.; Veldem, W.E.V., Generating parity relations for detecting and identifying control system component failures, J. guidance control and dynamics, 11, 60-65, (1988) · Zbl 0658.93025 |

[10] | O’Reilly, J., Observers for linear systems, (1983), Academic Press London · Zbl 0513.93001 |

[11] | Park, J.; Stein, J.L., Closed-loop, state and input observer for systems with unknown inputs, Internat. J. control, 48, 1121-1136, (1988) · Zbl 0659.93007 |

[12] | Stein, J.L.; Park, J., Measurement signal selection and a simultaneous state and input observer, ASME J. dynam. systems meas. control, 110, 151-159, (1988) · Zbl 0647.93014 |

[13] | Vidyasagar, M., Control systems synthesis: A factorization approach, (1985), M.I.T. Press Cambridge, MA · Zbl 0655.93001 |

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