Global consensus of positive fractional‐order multiagent systems on directed graphs with input saturation

This paper investigates the consensus control of positive fractional‐order multi‐agent systems (FOMASs) with input saturation over directed graphs that contain at least one spanning tree. Firstly, an observer‐based protocol for positive consensus is proposed, offering larger design flexibility than the classical Luenberger observer‐based protocol while taking both input saturation and the positive constraint into account. Secondly, sufficient conditions for positive consensus are established by using positive system theory and the properties of the Caputo fractional derivative. These conditions in terms of linear matrix inequalities (LMIs) are less conservative since they only involve the number of nodes in directed graphs. Additionally, the consensus problem for FOMASs with uncertain parameters is examined via using the properties of the Metzler matrix. Unlike many consensus problems with input saturation that achieve semiglobal consensus, the obtained results in this paper achieve global consensus. Subsequently, the feedback matrix and the gain matrix are solved by an iterative LMI algorithm. Finally, the given results are verified through a practical model of electrical circuits and numerical simulations.