$\mathbf{H}\infty$ Group Consensus Control for Directed Nonlinear Multi-agent Systems

$\mathrm{H}\infty$
group consensus control for nonlinear multi-agent systems is investigated. Lipschitz nonlinear items and external disturbance are considered for high order multi-agent systems. Based on in-degree balance, both the Laplacian matrix and group consensus matrix of the directed system can be decomposed as a product of transforming matrix and another special matrix. The transforming matrix can turn the group consensus problem into a stability problem. Designing group consensus variables and a H performance index, and utilizing Lyapunov method as well as the linear matrix inequality, the correctness of the designed control inputs is theoretically proved. Simulation result presents the effectiveness of the algorithm.