Abstract: For the uncertain time-delay systems, the uncertain time-delay power system model is established based on the constant time-delay power system model. By using Bessel-Legendre inequality method to deal with the integral term in the derivative of the new augmented Lyapunov-Krasovskii functional, an uncertain delay stability criterion with less conservativeness is obtained. Compared with the existing literature, the superiority of the proposed method is verified. According to the obtained stability criteria, the memoryless feedback controller and the feedback controller with memory are designed by parameter adjustment method and LMI technology. The stabilization of the controllers is verified by the analysis of the typical second-order delay system and the single machine infinite bus system.