H_∞ group consensus of linear dynamical systems under directed switching topology

This brief investigates the H_∞ group consensus problem for linear dynamical systems with directed switching topology and external disturbance. The H_∞ group consensus problem for multiagent systems (MASs) is complicated since the agents from different clusters may be cooperative or competitive. By using together algebraic graph theory and Lyapunov stability theory, we first analyze the stability of group consensus with desired H_∞ performance, and then establish a sufficient condition to achieve the H_∞ group consensus. This sufficient condition is derived in terms of the strengths of intra-cluster couplings and the solution to an algebraic Riccati equation, whose solvability can be guaranteed if the MAS is state feedback stabilized with a bounded L₂ gain. Moreover, the lower bound of the inter-cluster coupling strength and dwell time are explicitly specified. Finally, the effectiveness of the theoretical results is verified by a numerical example.