Consensus of Fractional-Order Fuzzy Multiagent Systems: Exploring Impulsive Security Protocols

This article investigates impulsive security protocols with the goal of achieving consensus of fractional-order fuzzy multiagent systems (FOFMASs). In contrast to multiagent systems characterized by ordinary differential equations, FOFMASs are created using Takagi–Sugeno fuzzy rules and fractional-order differential equations, which allow for nonlinearities with parameter uncertainties and also manage memory effects. Due to the potential of denial-of-service (DoS) attacks, the topology among nodes may change, and it is necessary to gain insight into the security consensus under topology switching. This article tackles the security protocol problem by designing a distributed impulsive control for each agent, relying on global delayed communications and topology switching resulting from DoS attacks. Analyzing the stability of impulse-free error systems is a salient problem. Supported by the Lyapunov method and average impulsive interval method, for two cases of self-stabilization or instability of the error system in the absence of impulse, some sufficient conditions are presented to ensure the exponential consensus of FOFMASs under distributed impulsive control with communication delays. Besides, several corollaries are provided to guarantee the consensus under distributed impulsive control without communication delays. Finally, two numerical examples are provided, and some numerical simulations are given to confirm the efficacy of the theoretical findings.