Actuator and sensor fault detection for a nonlinear fractional-order system with time-varying delay

In this paper, the problem of actuator and sensor fault detection for a nonlinear fractional-order system with time-varying delay is investigated. An observer-based multi-objective fault detection method is proposed for nonlinear fractional-order systems. This method integrates a quadratic function with a Caputo derivative estimation lemma to effectively address nonlinearities, external disturbances, and simultaneous actuator/sensor faults. In order to detect the faults, a memoryless full-order observer is employed as the residual generator. Subsequently, by employing the Razumikhin theorem concerning Caputo derivative estimation of quadratic functions in conjunction with the model-related Lyapunov function technique, sufficient conditions are derived to ensure the asymptotic stability of the error system with an pre-described $H_{\infty }/H_{-}$ performance, thereby simultaneously ensuring robustness against disturbances and sensitivity to faults. Finally, an illustrative example is presented to demonstrate the effectiveness of the proposed results.