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∞ 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∞ 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∞ 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∞ observer technique.