Robust H ∞ Group Consensus for Interacting Clusters of Integrator Agents

In this technical note, we investigate the H ∞ group consensus for networks of agents modeled by single-integrator with model uncertainty and external disturbance. By developing tools from algebraic graph theory, matrix analysis as well as Lyapunov stability theory, we are able to derive some sufficient conditions in terms of the structure and strength of the couplings among agents so as to guarantee the group consensus with desired $H-{\infty }$ performance. Such conditions are structural and easy to check. Furthermore, some adaptation laws are proposed to address the coupling strength problem arising from the consideration that the theoretical value is usually much larger than expected in practice. Finally, some simulation examples are presented to demonstrate the efficiency of the theoretical findings.