Secure Synchronization of Lur’e Systems Under DoS Attacks With Application to Chua’s Circuit: Aperiodic Sampled-Data Control

This article explores a novel secure synchronization scheme for drive-response Lur’e systems under denial-of-service (DoS) attacks. The main innovative features are characterized by an aperiodic transmission mechanism without attack detection, a resilient sampled-data control linked with timer, and a highly aperiodic-interval-dependent Lyapunov functional. The output error of the drive-response system is aperiodically sampled and transmitted through networks subject to DoS attacks. By applying a timer, this aperiodic transmission mechanism assesses whether the aperiodic sampled-data characteristic is impacted by attacks at any time, thus avoiding the need for attack detection and enhancing its practicality. Correspondingly, a resilient sampled-data control linked with timer is developed, wherein the control signal dynamically changes when not impacted by attacks, improving secure control performance for achieving synchronization. Additionally, a new secure synchronization standard compatible with this scheme is introduced. Based on the framework, secure synchronization analysis and control results are derived through the proposed highly aperiodic-interval-dependent Lyapunov functional. More specially, the matrix variables in this functional are explicitly related to each aperiodic sampling transmission interval, as well as those used for handling nonlinear functions, which contributes to reduced conservativeness in the results. The theoretical advantages of these new methods and results are compared with existing literature. Finally, the novel secure synchronization scheme is applied to two examples to validate the effectiveness and superiority, including a 3-neuron neural network and a chaotic Chua’s circuit.