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This paper investigates the consensus problem for the distributed multiagent system (MAS), where the trajectory of each agent is displayed by curvature and torsion, and the communication behaviors among agents are influenced by time delay and corrupted by noises. According to the Frenet–Serret formulas, a class of consensus protocols is designed for all agents, and a closed-loop system is obtained. Based on the Lyapunov method, several consensus criteria are derived, where the consensus criteria are characterized by curvature functions and torsion functions. Finally, one example shows the reliability of the proposed methods.

Curvature- and Torsion-Based Consensus for the Markovian Switching Multiagent System with Communication of Noise Disturbance and Time Delay