In this paper, the annulus-event-based fault detection, isolation and estimation (FDIE) problem is examined for a class of multi-rate time-varying systems with sensor degradations as well as unknown but bounded disturbances and faults. A new event-triggered communication mechanism is proposed under which the measurement signal is transmitted to the observer/estimator only when the relative error satisfies certain triggering-annulus. By employing the set-membership estimation method, we design the time-varying annulus-event-based fault detection estimator (AEFDE), fault isolation estimator (AEFIE) as well as fault estimator (AEFE) with the help of recursive matrix inequalities. Based on the obtained AEFDE, AEFIE and AEFE, a residual evaluation function method is first employed to detect the fault, a novel estimation-error-function matching approach is then developed to isolate the fault, and the extended vector technique is finally adopted to estimate the fault. Especially, two subsequent optimization problems are investigated, one is to seek the minimal ellipsoidal region for the best estimation performance, and the other is to minimize the triggering-annulus so as to reduce the triggering frequency with guaranteed estimation performance. A numerical simulation example on a three-tank system is employed to show the effectiveness of FDIE scheme proposed in this paper. (C) 2018 Elsevier Ltd. All rights reserved.