Optimization and H∞ Performance Analysis for Load Frequency Control of Power System with Transmission Delay Under DoS Attacks

This paper addresses the stability and H∞ performance of a single-area discrete-time power system with time-varying transmission delays under Denial-of-Service (DoS) attacks. First, the power system is modeled as a discrete-time delay system that integrates both DoS-induced delays and transmission delays, with PI controllers incorporated for Load Frequency Control (LFC). Using advanced summation inequality techniques, a Lyapunov–Krasovskii Functional (LKF) is constructed to capture comprehensive system state information, enabling the derivation of less conservative stability criteria. The proposed stability criterion based on linear matrix inequalities (LMI) ensures asymptotic stability and meets the H∞ performance index, while considering norm-bounded external load disturbances. Two convex optimization algorithms are designed to obtain optimal controller gains, either for a given H∞ index or by searching within a specified index range. Numerical examples and MATLAB simulations validate the effectiveness of the method. The results demonstrate that the maximum allowable delay upper bounds (MADUBs) estimated by the proposed criterion are larger than those obtained by existing methods, with an increase of at least 1 s. This indicates a reduction in conservatism. Simulation trajectories of frequency deviation (Δf) and area control error (ACE) confirm that the system remains stable under DoS attacks, with responses converging to zero after transient oscillations.