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

Abstract

SummaryThis 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.