Stabilisation for a wave equation with distributed time delay in the internal input

This paper analyzes the stabilization problem of a wave equation subject to distributed time delay in the internal input. Based on a partial state predictor, we design a feedback control signal which is shown to stabilize an undelayed system by the spectral analysis and the Hilbert uniqueness method. The stability of the original system under the feedback control is obtained via the relation between the original system and the undelayed system in terms of stability.