Event-triggered Group Consensus for First-order Multi-agent Systems Based on Directed Topology

Abstract

Event-triggered group consensus problem is addressed in this paper. Based on the assumption named the in-degree balance, a directed first-order multi-agent system is constructed, which consists of two subgroups. To analyze the problem, the Laplacian matrix of the initial system is decomposed to be two matrices with less row and column dimension. Then the initial state vector can be substituted by a new one, each element in which is the error of two adjacent elements of the initial state vector. Then a new reduced-order system is constructed and the consensus problem is converted to a stability problem. With the designed Lyapunov function, the validity of the proposed algorithm is proved. The lower-bound of the inter-event time interval is also presented. Simulation results are presented to demonstrate the effectiveness of the protocol.