Robust consensus of fractional multi-agent systems with external disturbances

Abstract

In this paper, the problem of robust consensus for fractional multi-agent systems with external disturbances is investigated over a directed fixed interaction graph. Based on Mittag-Leffler stability theory and the inequality techniques, both linear and nonlinear systems are considered. Firstly, for fractional linear multi-agent systems, 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. Secondly, for fractional nonlinear multi-agent systems, a pinning control input is proposed such that robust consensus can be realized. Finally, the numerical simulations are given to verify the correctness of the presented theories.