H−/L∞ UIO‐based fault detection and isolation design in finite‐frequency domain for nonlinear systems

Abstract

The issue of fault detection and isolation design in the finite‐frequency domain for discrete‐time Lipschitz nonlinear systems subjected to actuator faults and disturbances is investigated. A bank of H−/L∞ unknown input observers (UIOs) is established using the generalized observer scheme to generate residuals that are insensitive to a specific actuator fault but sensitive to the other actuator faults. Furthermore, in the finite‐frequency domain, the H− and L∞ performance indices are simultaneously used to improve the fault detection sensitivity and attenuate the influence of disturbances on the residuals, respectively. The design conditions for the bank of H−/L∞ UIOs are derived from the generalized Kalman–Yakubovich–Popov lemma and converted into an optimization problem constrained by linear matrix inequalities to solve the design matrices more easily. To diagnose actuator faults, a fault detection and isolation scheme is established using the time‐varying threshold from the L∞ performance analysis. Finally, the effectiveness of the fault detection and isolation scheme using the bank of H−/L∞ UIOs is validated by the simulation of two examples.