Relaxed convergence conditions for multi-agent systems under a class of consensus algorithms

This paper presents sufficient conditions for the convergence for a group of single integrator agents with a directed and static information flow graph, under a special class of control inputs. Using a novel approach based on the smallest order of the nonzero derivative, it is shown that under some mild conditions the convex hull of the agents will be contracting. The finite intersection property is then used to prove the convergence of the agents to a common fixed point. The results obtained in this work are more general than the ones reported in the literature. An illustrative example is provided to verify the proposed convergence conditions.