Robust consensus for fractional nonlinear multi-agent systems with external disturbances

Abstract

In this paper, robust consensus for fractional nonlinear multi-agent systems with external disturbances is investigated over a directed fixed interaction graph. Mittag-Leffler stability and the general algebraic connectivity are introduced to establish various sufficient conditions for reaching consensus. For fractional multi-agent systems with nonlinear dynamics, when the condition on the general algebraic connectivity is satisfied, it is shown that consensus can be achieved asymptotically in the absence of disturbances. In the presence of disturbances, the steady-state errors of any two agents can reach a small region determined by the bound of disturbances. Rigorous proof is given by using fractional Lyapunov theory and graph theory. Finally, the numerical simulations are given to verify the correctness of the presented theory.