Fault Detection for T-S Fuzzy Time-Delay Systems: Delta Operator and Input-Output Methods

This paper focuses on the problem of fault detection for Takagi-Sugeno fuzzy systems with time-varying delays via delta operator approach. By designing a filter to generate a residual signal, the fault detection problem addressed in this paper can be converted into a filtering problem. The time-varying delay is approximated by the two-term approximation method. Fuzzy augmented fault detection system is constructed in δ-domain, and a threshold function is given. By applying the scaled small gain theorem and choosing a Lyapunov-Krasovskii functional in δ-domain, a sufficient condition of asymptotic stability with a prescribed H
_∞
disturbance attenuation level is derived for the proposed fault detection system. Then, a solvability condition for the designed fault detection filter is established, with which the desired filter can be obtained by solving a convex optimization problem. Finally, an example is given to demonstrate the feasibility and effectiveness of the proposed method.