H∞$$ {H}_{\infty } $$ Filter Design for Load Frequency Control Systems With Limited Communications and Cyber Attacks as Well as Probabilistic Interval Delays

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ABSTRACT This paper investigates the design of filters for load frequency control (LFC) systems, considering factors such as packet loss, spoofing attacks, and probabilistic interval delays. Firstly, to better reflect the uncertainty of communication delays in practical scenarios, the filter design process incorporates the probability distribution of these delays. Given the limitations in information transmission that can degrade system performance and lead to instability, the paper also addresses the impact of packet loss and network attacks in the communication channel. Secondly, an filtering error model is developed for an LFC system, accounting for packet loss, network attacks, and probabilistic interval delays. Based on this model, a sufficient condition for ensuring the performance index of the proposed filtering error system is derived using Lyapunov stability theory. Finally, the theoretical results are validated through numerical simulations.

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