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This paper investigates a resilient event-triggering H\infty load frequency control (LFC) for multi-area power systems with energy-limited Denial-of-Service (DoS) attacks. The LFC design specifically takes the presence of DoS attacks into account. First, an area control error dependent time delay model is delicately constructed for multi-area closed-loop power systems. Second, a resilient event-triggering communication (RETC) scheme is well designed, which allows a degree of packet losses induced by DoS attacks and has the advantage of improving the transaction efficiency. Then, by using the Lyapunov theory, two stability and stabilization criteria for the multi-area power systems are derived under consideration of the energy-limited DoS attacks. In these criteria, the relationship between the allowable DoS attack duration and the resilient event-triggering communication parameters are clearly revealed. Moreover, an algorithm is also provided to obtain the RETC parameters and the LFC gains simultaneously. Finally, a case study shows the effectiveness of the proposed method. [ABSTRACT FROM PUBLISHER]