Wide-area control is highly efficacious for maintaining sufficient damping of the low-frequency oscillations in the power system. The Wide-Area Measurement System (WAMS) provides wide-area signals to the control site through a communication channel. Even though the wide-area signal improved the dynamic behavior of the power system, a time delay usually exists during the transmission, which is unavoidable. The damping performance of the power system is degraded due to the time delay. In this paper, synchronized and non-synchronized feedback configurations are considered, and the time delay margin is calculated. The Lyapunov theory is adopted for investigating the synchronous and non-synchronous delay-dependent stability criteria for the power system. A lead–lag and a robust H∞ wide-area damping controller (WADC) are proposed to measure the delay margin for synchronized and non-synchronized delay feedback. The relationship between the damping performance and the delay margin is established. It is observed that a non-synchronous feedback-based controller can endure a larger time delay variation than a synchronous feedback-based controller. The nonlinear simulation is carried out to verify the effectiveness of the proposed controllers in Kundur’s two-area system and the IEEE-39 bus test system.