Stabilizability and Bipartite Containment Control of Multi-Agent Systems Over Signed Directed Graphs

This paper investigates the stabilizability and bipartite containment control problem of general linear multi-agent systems over signed directed graphs, where the negative edges indicate the antagonistic interactions between agents. By employing the proposed bipartite containment control protocols over signed directed graphs, and combining the linear system stabilization theory and the signed Laplacian matrix, the necessary condition for the stabilization of multi-agent systems with multiple leaders is discussed. According to this necessary condition, a leader-follower matching method is presented to establish leader-follower multi-agent system networks. Based on the leader-follower topology established above and the designed state feedback gain, the stability of multi-agent systems is proved by using the system error and the algebraic Riccati equation. It is shown that the followers can gradually converge into the convex hull spanned by the states and the sign-inverted states of leaders, and the bipartite containment control of multi-agent systems can be realized. The simulation results verify the feasibility of the theoretical analysis.