To address the problem of frequency stability of a multi-region power system with new energy, a sampling load frequency control scheme considering the changes of the control signal update period is proposed. First, a new power system sampling LFC model is constructed considering the sampling characteristics of the system. The model is transformed into a sampling data network control system. Then, by employing information of the whole sampling interval , a new two-side loop Lyapunov function is established. Combining the proposed Lyapunov function and a free-matrix-based inequality, a less conservative stability criterion is derived for the system. Using this criterion, a design algorithm for the desired sampling controller is proposed to ensure system stabilization. Finally, the validity and superiority of the proposed method are verified by simulation. This work is supported by the National Natural Science Foundation of China (No. 52061130217).