Graph Laplacian and Lyapunov design of collective planar motions

In recent work, the authors have proposed a Lyapunov design to stabilize isolated relative equilibria in a kinematic model of identical all-to-all coupled particles moving in the plane at unit speed. This note presents an extension of these results to arbitrary connected topologies by considering a general family of quadratic Lyapunov functions induced by the Laplacian matrix of the communication graph.

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