Matrix-weighted consensus of fractional-order networked systems via sampled-data control

This paper addresses the consensus in fractional-order networked systems with matrix-weighted coupling, where the interactions of agents are characterized by positive definite or positive semi-definite matrices. A distributed sample-based control strategy is designed, in which each agent updates its state using sampled data. Some necessary and sufficient consensus conditions are derived for both undirected and directed matrix-weighted networks, respectively. The conditions depend on the sampling period, the fractional order, the control gain strengths, as well as the eigenvalue properties of the matrix-weighted Laplacian. Notably, for undirected networks, consensus is closely related to the null space of the matrix-weighted Laplacian. For directed networks, the existence of a positive spanning tree is not necessary to reach matrix-weighted consensus. Finally, simulation examples are conducted to validate the effectiveness of the theoretical analysis.