Sign consensus of heterogeneous linear multi-agent systems without an explicit leader

This paper investigates leaderless output sign consensus of heterogeneous linear multi-agent systems over fixed di-rected signed graphs. The multi-agent system can synchronize in the same sign concurrently with time-varying values without an explicit leadership. Established on the assumption that the adjacency matrix of the signed graph is eventually positive, a virtual leader is constructed by utilizing a distributed sign observer. This virtual leader is not pre-specified but arises from the graph topology and the initial states of the agents. In light of this distributed sign observer, we propose a state feedback controller that drives the outputs of such multi-agent systems to reach sign consensus.