Fuzzy Fault Detection Filter Design for T–S Fuzzy Systems in the Finite-Frequency Domain

This paper deals with the fault detection filter design for a nonlinear discrete-time system in the Takagi-Sugeno fuzzy form with faults and unknown inputs. Both unknown input and fault frequencies are assumed to be known and to reside in low-/middle-/high-frequency ranges. A filter is proposed in the finite-frequency domain to reduce the conservatism generated by those designed in the entire-frequency domain. In order to guarantee the best robustness to disturbances and sensitivity to faults, the developed filter combines the H_/H
_∞
performances. The asymptotic stability of the filtering error dynamics is ensured by using a fuzzy Lyapunov function and a linear matrix inequality approach. Finally, two examples are presented to validate the proposed new design techniques.