In this study, a delay-dependent anti-windup compensator (AWC) is designed for supplementary damping control (SDC) of flexible AC transmission system (FACTS) device to enhance the damping of inter-area oscillations of the power system subjected to time-delay and actuator saturation. By employing global signal measurements, an SDC of FACTS device is designed without considering the effect of time-delay and actuator saturation to stabilise the power system using a robust output feedback controller with pole placement approach. Then, based on the generalised sector condition and Lyapunov–Krasovskii functional, an add-on delay-dependent AWC is designed to mitigate the adverse effect of time-delay and actuator saturation non-linearity. For the design of delay-dependent AWC, sufficient conditions guarantee the asymptotic stability of the closed-loop power system are formulated in the form of linear matrix inequalities (LMIs). These conditions are cast into the LMI-based convex optimisation problem to compute the AWC gains. To evaluate the effectiveness of the proposed controller, non-linear simulations were performed first using MATLAB/Simulink. Then, the authors implemented the proposed controller in real-time using the Opal-RT digital simulator. From the obtained results, it is observed that the proposed controller enhances the damping of inter-area oscillations by compensating the effect of time delay and actuator saturation.