Stability of Open Multi-agent Systems over Dynamic Signed Digraphs

Abstract: We address the synchronization problem in open multi-agent systems (OMAS) containing both cooperative and antagonistic interactions. In these systems, agents can join or leave the network over time, and the interaction structure may evolve accordingly. To capture these dynamical structural changes, we represent the network as a switched system interconnected over a dynamic and directed signed graph. Additionally, the network may contain one or multiple leader groups that influence the behavior of the remaining agents. In general, we show that the OMAS exhibit a more general form of synchronization, including trivial consensus, bipartite consensus and containment. Our approach uses the signed edge-based agreement protocol, and constructs strict Lyapunov functions for signed networks described by signed edge-Laplacian matrices containing multiple zero eigenvalues. Numerical simulations validate our theoretical results.