Grid-forming control can provide inertia support for the system and improve system stability.However,grid forming control relies on digital control technology and has control delay problems,which can have a certain impact on system stability.This paper first establishes a state space model of a networked inverter system considering control delay,and then constructs a Lyapunov-Krasovskii(L-K)functional.Based on the second-order Bessel Legendre inequality,the integral term generated during the derivative process of the L-K functional is processed.The Lyapunov stability theorem is used to obtain a delay stability criterion with lower conservatism,and the delay stability margin of the system is solved through linear matrix inequality.The simulation results have verified the correctness and effectiveness of the proposed method for solving time-delay stability margin,and compared with other methods,it has lower conservatism,and further analyzed the influence of control parameters on the stability of both non time delay systems and time delay systems.Measures to improve the time delay stability of grid-forming inverter systems have been proposed.