Algebraic criteria for second-order global consensus in multi-agent networks with intrinsic nonlinear dynamics and directed topologies

This paper discusses the second-order globally nonlinear consensus in general multi-agent directed networks with both non-time-delay and time-delay couplings. Some easily manageable delay-independent algebraic criteria are presented to unravel the underlying mechanics for reaching the second-order consensus. The obtained results are associated with the underlying network interactive topologies, inner coupling matrices and coupling gains between agents. Theoretical derivation is complemented by its validation on a simulation example.