Necessary and sufficient conditions for consensus of multi-agent systems with nonlinear dynamics and variable topology

This paper studies some necessary and sufficient conditions for consensus of continuous multi-agent systems with nonlinear node dynamics and variable topology. The multi-agent systems are under variable topology. Basic theoretical analysis is carried out for the case where for each agent the nonlinear dynamics are governed by the position terms of the neighbor nodes. A necessary and sufficient condition associated with eigenvalues is given to ensure consensus of the nonlinear multi-agent system. Based on this result, a simulation example is given to verify the theoretical analysis.