In view of a solution of the problem of asymptotic stability of LFC system, a mathematical model has thus been established of time delay LFC system with PID parameters in the system matrix. By selecting Lyapunov-Krasovskii functional of delay product type, the functional derivative can be defined with the extended inverse convex quadratic inequality method adopted, thus obtaining a new criterion of robust stability for LFC systems with a lower conservation. Finally, an experimental simulation is carried out with given practical examples, with the simulation verifying verify the effectiveness and superiority of the proposed new criteria.