<i>H</i> _∞ Fuzzy Control for a Class of Cyber-Physical Systems Under Frequency-Duration-Constrained Replay Attacks

In this article, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> fuzzy control problem is investigated for a class of nonlinear systems subject to replay attacks with frequency-duration constraints. Owing to the vulnerability of the open shared communication network, the information transmitted from the sensor to the controller may be exposed to replay attackers. A novel yet comprehensive replay attack model is constructed to characterize the repeated replay behavior of the adversary. On the basis of the constructed model, a fuzzy controller is designed to guarantee asymptotic stability and the desired <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance. By employing Lyapunov stability theory and the orthogonal decomposition technique, sufficient conditions are derived to ensure the existence of the desired controller parameter. Finally, simulation results are presented to verify the effectiveness and correctness of the proposed fuzzy controller for T-S fuzzy systems under replay attacks.