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This paper is dedicated to a proportional–integral intermediate estimator based fault-tolerant control method for Markov jump systems with event-triggered inputs. A proportional–integral type intermediate estimator is established to reconstruct sensor and actuator faults, as well as system states. A dynamic event-triggered mechanism is designed to reduce unnecessary transmissions between the controller and the actuator. A threshold-dependent fault-tolerant controller is established to actively compensate for actuator faults. Finsler's lemma is adopted to decouple the control gain, the observer gain and the Lyapunov variable. At last, the proposed estimation method is verified by a comparison example. • A PI–type intermediate observer is designed to obtain better estimation performance. • A threshold-dependent triggering scheme is designed to reduce the network burden. • A structured separation method is adopted to address complex couplings between gains. [ABSTRACT FROM AUTHOR]