H ∞ performance for load frequency control systems with random delays

Abstract

This paper investigates the problem of performance analysis for PI-type load frequency control (LFC) of power systems with random delays. By taking the probability distribution characteristic of communication delays into account in the LFC design, the power systems with a PI controller are modelled as stochastic time-delay systems. Furthermore, a delay-product-type augmented Lyapunov-Krasovskii functional (LKF) is constructed, and a new extended reciprocally convex matrix inequality combining Wirtinger-based integral inequality with convex combination approach is utilized to reduce the conservatism of main results. As a result, less conservative performance criteria are derived, which guarantee the asymptotically stable in the mean-square of the considered systems. Numerical examples are also provided to illustrate the superiority of our proposed methods.