Consensus of second-order nonlinear multi-agent systems under state-controlled switching topology

This paper studies the consensus problem of second-order multi-agent systems under both fixed and switching directed topologies in a more general framework. Specifically, each agent incorporates an intrinsic nonlinear dynamics and the communication topology switches in a state-controlled manner. Novel distributed consensus protocols are proposed based only on relative position information and local velocity information. Through constructing appropriate Lyapunov functions, it is shown that the proposed protocols are feasible for achieving consensus, even under switching topology jointly containing a spanning tree. Moreover, some easily manageable algebraic criteria are presented to unravel the underlying mechanism for reaching consensus. In the special case of multi-agent systems with double-integrator dynamics, we further derive a necessary and sufficient condition for the consensus problem. Finally, two numerical examples are provided to validate the effectiveness of theoretical results.