Fault detection observer design for discrete-time 2-D T-S fuzzy systems with finite-frequency specifications

This work designs a fault detection observer for two-dimensional (2-D) non-linear systems having discrete dynamics expressed in Takagi-Sugeno (T-S) form. The finite frequency (FF) domain is considered during designing the observers, which makes them different from previously proposed 2-D detection observers. Faults and disturbances are considered in two different FF domain intervals, respectively. Fault sensitivity and disturbance robustness are measured by two FF performance indices. The aim here is to formulate an observer that assures the fault sensitivity and disturbance robustness of the residual error system. Essential lemmas have been proposed for nonlinear 2-D Roesser model, which are expected to serve as a bridge between two domains (frequency and time). Conditions have been provided, that are sufficient to design a desired fault detection fuzzy observer and effectivity of the proposed method is shown by simulation results.