Second-order consensus with unknown dynamics via cyclic-small-gain method

This study proposes a distributed non-linear consensus protocol for second-order non-linear multi-agent systems with unknown locally Lipschitz dynamics and connected graph. The main analysis is based on a blend of graph-theoretic and non-linear-theoretic tools with the notion of input-to-state stability (ISS) playing a central role. Through the backstepping design, the closed-loop multi-agent system is transformed into a two-cascade interconnected system with proven ISS properties. Correspondingly, the recently developed cyclic-small-gain theorem is then employed to guarantee the asymptotic stability of the closed-loop multi-agent system, which implies consensus.