Distributed H∞ and H2 consensus control in directed networks

In this study, the H_∞ consensus problem of a group of linear multi-agent systems with directed communication graph is addressed. To achieve H_∞ consensus, a new class of distributed consensus protocols based only on the relative states of the neighbouring agents is proposed. Compared with the existing protocols, the one presented in this study focuses on solving the H_∞ consensus problem in strongly connected directed networks. By using tools from algebraic graph theory and Lyapunov stability analysis, it is theoretically shown that distributed H_∞ consensus in the closed-loop multi-agent systems with strongly connected topology can be achieved if the distributed consensus protocol is appropriately designed. A two-step algorithm is then presented to construct such a protocol. The H₂ consensus problem for networked systems is further investigated. Finally, the effectiveness of the theoretical analysis is verified via numerical simulations.