Leader-follower consensus of uncertain variable-order fractional multi-agent systems

Abstract The leader-follower consensus of a class of variable-order fractional (VOF) uncertain linear multi-agent systems is studied in this paper. According to the stability theorem of VOF systems, by using the singular value decomposition of matrices and some related lemmas, a sufficient condition to obtain leader-follower consensus of uncertain VOF linear systems is proposed in the form of a linear matrix inequality. A control protocol is designed, which is dependent on the order of the VOF multi-agent system, reducing the conservatism of existing methods and being applicable to fixed-order and nonlinear VOF multi-agent systems. The feasibility and effectiveness of the approach are verified by using some numerical simulations.