With the increasing penetration rate of distributed power generation represented by Photovoltaic(PV) power generation, active distribution networks are facing issues such as reverse power flow and voltage violations. Due to the fact that the communication between PV inverter terminals and the central controller is an all-time, all-domain heterogeneous network, communication delays are inevitable, which can lead to degraded control performance and even system instability. To address these challenges, a control strategy for the active power of PV inverters is designed to adjust the power distribution in the distribution network and regulate node voltages. A linearized state-space model that accounts for communication delays is proposed, and a stability criterion depending on communication delays is obtained by using the Linear Matrix Inequality(LMI) method. This approach determines the delay margin to ensure the stable operation of the system. Simulation results demonstrate that the constructed state-space model and the calculated delay margin can effectively enhance the robustness of the system and are applicable to multiple PV systems in active distribution networks.