Resilient Finite-Time Consensus of Variable-Order Fractional Multiagent Systems Under DoS Attacks

This article aims to address the finite-time consensus issue for variable-order fractional multiagent systems (MASs) under denial of serve (DoS) attacks. First, the framework of node-based DoS attack is introduced, including its influences, detection, and recovery mechanisms. Second, a new variable-order fractional difference (VO-FD) inequality is proposed to accurately evaluate the variable-order fractional derivative of the power function. Based on the developed inequality, two novel finite-time stability theorems are presented based on the developed inequality, which fill up the gap in variable-order fractional finite-time stability without and with DoS attacks, respectively. Third, a resilient distributed control protocol is proposed, where the dynamic event-triggered mechanism (DETM) is introduced based on the detected signal of attack to ensure the desired control performance and economize system resources. According to the Lyapunov stability theory, the consensus can be achieved within the settling time, and some linear matrix inequality (LMI)-based conditions are obtained. Finally, the feasibility and validity of theoretical analysis is illustrated by simulation example.