The robust fusion estimation problem of a multi-sensor system with communication constraints, random packet drops, d-step state delays, and deterministic control inputs is investigated. The state augmentation method is used to transform the time delay system into a non-time delay system, and then a robust fusion estimation algorithm based on sensitivity penalty is proposed and the pseudo-cross-covariance matrix is updated. An event-triggered robust fusion estimator with state delay and deterministic control inputs is considered to make the model closer to reality while effectively reducing network congestion and lowering communication costs. Conditions are given to ensure that the estimation errors of the robust fusion estimator are uniform boundedness. Two sets of numerical simulations are provided to illustrate the effectiveness of the derived fusion estimator.