Nonlinear second-order multi-agent systems subject to antagonistic interactions without velocity constraints

Abstract

This paper studies the nonlinear second-order multi-agent systems without velocity information while subject to antagonistic interactions among the reciprocal agents. When being free of nonlinear disturbances, a necessary and sufficient condition for the consensus (resp. stability) problem is presented, which essentially shows that the coupling weights and topology structure suffice to assure the consensus (resp. stability) of the agents. Whereas, nonzero eigenvalues of the Laplacian matrix also act a crucial role, provided that merely the absolute information of the auxiliary variable is demanded. The derived results implicitly manifest that structurally balanced graph (resp. isolated structurally balanced graph or containing the in-isolated structurally balanced subgraph) is merely the necessary condition for the consensus (resp. stability) of the agents within the second-order dynamical setting. In the presence of nonlinear dynamics, we explicitly extend the derived results with the help of the Lyapunov-based technique under quite mild assumptions. Furthermore, some comparisons are presented in contrast to some of the existing literature. Finally, numerical examples are given to validate the efficiency of the obtained results.