Finite-time group consensus for nonlinear heterogeneous fractional-order multi-agent systems with communication disturbances

This paper studies the finite-time group consensus problem of nonlinear heterogeneous fractional-order multi-agent system (FOMAS) with communication disturbances. Without the inter-group balance condition, a class of distributed control protocols is proposed by combining the information of neighbouring agents and their corresponding group consensus goals. By using the Kronecker product and the LMI technique, a linear FOMAS composed of the group consensus error and communication disturbance variables is obtained to describe the original system. Then, by constructing a suitable fractional-order Lyapunov function, sufficient conditions are presented to analyse the stability of the consensus error system in finite time. Moreover, it provides the upper bound of the convergence time for the group consensus. Finally, simulation examples are presented to demonstrate the effectiveness of the proposed scheme and theoretical results.