Necessary and Sufficient Conditions for Consensus in Fractional-Order Multiagent Systems via Sampled Data Over Directed Graph

This paper studies the consensus in fractional-order multiagent systems over directed graph via sampled-data control method. A distributed control protocol using the sampled position and velocity data is designed. By virtue of the Mittag-Leffler function, Laplace transform, and matrix theory, some necessary and sufficient conditions associated with the sampling period, the fractional order, the coupling strengths, and the network structure to obtain consensus of the systems are obtained. Then, some detailed discussions are presented about how to select the sampling period and how to design the coupling strengths to attain the consensus of the systems, respectively. Lastly, some numerical simulation results are illustrated to reflect the availability of the theoretical analysis.

Automated summary

This paper explores consensus in fractional-order multiagent systems over directed graphs using a sampled-data control method. A distributed control protocol is designed utilizing sampled position and velocity data. Necessary and sufficient conditions for achieving consensus are derived, along with discussions on selecting sampling periods and designing coupling strengths. Numerical simulations confirm the theoretical analysis.