Positive consensus of fractional-order multi-agent systems

This paper considers the positive consensus of fractional-order multi-agent systems described by general linear dynamics with the fractional order belonging to (0, 2) via state feedback. Firstly, the distributed positive consensus protocols are given, and then, the necessary and sufficient conditions are gained for the consensus with positive constraint based on the fractional-order stability theory as well as the features of Metzler matrix. Furthermore, some sufficient positive consensus conditions are provided and are reduced to the conditions without the global networked information for the system with $$\alpha \in (0,1]$$ . Finally, illustration examples are provided to indicate not only the validity but also the superiority of the presented approach, compared with the highly related methods.