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

Abstract

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 L 2 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.

Gain margin and Lyapunov analysis of discrete‐time network synchronization via Riccati design

“…14 The continuous-time synchronization problem with a directed switching topology is solved by Saboori and Khorasani 15 and Wen and Zheng, 16 where the non-diagonal graph weighting matrix is a positive definite matrix solved from a continuous-time Lyapunov matrix inequality involving the graph Laplacian. The problem of group consensus is investigated in the work of Ren et al, 17 where continuous-time Riccati design and Lyapunov analysis is applied to in-degree balanced networks.…”