## Abstract

This letter deals with the fault detection and isolation (FDI) problem for linear structured systems in which the system matrices are given by zero/nonzero/arbitrary pattern matrices. In this letter, we follow a geometric approach to verify solvability of the FDI problem for such systems. To do so, we first develop a necessary and sufficient condition under which the FDI problem for a given particular linear time-invariant system is solvable. Next, we establish a necessary condition for solvability of the FDI problem for linear structured systems. In addition, we develop a sufficient algebraic condition for solvability of the FDI problem in terms of a rank test on an associated pattern matrix. To illustrate that this condition is not necessary, we provide a counterexample in which the FDI problem is solvable while the condition is not satisfied. Finally, we develop a graph-theoretic condition for the full rank property of a given pattern matrix, which leads to a graph-theoretic condition for solvability of the FDI problem.

Original language | English |
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Article number | 9094642 |

Pages (from-to) | 874-879 |

Number of pages | 6 |

Journal | IEEE Control Systems Letters |

Volume | 4 |

Issue number | 4 |

DOIs | |

Publication status | Published - Oct-2020 |

## Keywords

- Linear systems
- Observers
- Control theory
- Fault detection
- Indexes
- Controllability
- Silicon
- fault diagnosis
- linear systems
- FAILURE-DETECTION
- SENSOR-LOCATION
- DIAGNOSIS