Finite-Frequency H_ /H∞ Fault Detection for Discrete-Time T-S Fuzzy Systems With Unmeasurable Premise Variables

This paper investigates a finite-frequency H_/H-infinity fault detection method for discrete-time T-S fuzzy systems with unmeasurable premise variables. To minimize the effect of uncertainties on system performance and maximize that of actuator faults on the generated residual, both the H-infinity disturbance attenuation index and finite-frequency H_ fault sensitivity index are utilized. Since the premised variables are unmeasurable, the existing generalized Kalman-Yakubovich-Popov lemma cannot be directly extended to these nonlinear systems. In this paper, the conditions of allowing one to design the proposed H_/H-infinity fault detection observer are established and transformed into linear matrix inequalities. Some scalars and slack matrices are introduced to bring extra degrees of freedom in observer design. Finally, a single-link robotic manipulator model is utilized to illustrate that the proposed technique can detect faults with smaller amplitude than that required by a normal H-infinity observer technique.

Automated summary

This paper proposes a finite-frequency H_/H-infinity fault detection method for discrete-time T-S fuzzy systems. By utilizing disturbance attenuation and fault sensitivity indices, and transforming the design conditions into linear matrix inequalities with extra degrees of freedom, faults with smaller amplitude can be detected compared to conventional methods.