Design of robust fuzzy fault detection filter for polynomial fuzzy systems with new finite frequency specifications

This paper investigates the problem of fault detection filter design for discrete-time polynomial fuzzy systems with faults and unknown disturbances. The frequency ranges of the faults and the disturbances are assumed to be known beforehand and to reside in low, middle or high frequency ranges. Thus, the proposed filter is designed in the finite frequency range to overcome the conservatism generated by those designed in the full frequency domain. Being of polynomial fuzzy structure, the proposed filter combines the H−/H∞ performances in order to ensure the best robustness to the disturbance and the best sensitivity to the fault. Design conditions are derived in Sum Of Squares formulations that can be easily solved via available software tools. Two illustrative examples are introduced to demonstrate the effectiveness of the proposed method and a comparative study with LMI method is also provided.