Positive Consensus in Fractional-Order Interval Networked Systems

This brief investigates the positive consensus of fractional-order interval networked systems with the order $\alpha $ meeting $0 and $1 , respectively. Based on the theories of fractional stability and properties of Metzler matrix, by virtue of some rigorous theoretical analyses, the distributed control protocol is proposed and sufficient conditions of positive consensus for fractional-order interval networked systems with $0 are given, which have no connection with the order. What’s more, the results can be extended to conditions without using the information of Laplacian matrix with respect to networked topology. Furthermore, sufficient conditions for the systems with $1 to reach positive consensus are presented in terms of linear matrix inequality. Finally, simulation examples are given to verify the effective of results.