Graph Laplacian and Lyapunov Design of Collective Planar Motions

Rodolphe Sepulchre, Derek Paley and Naomi Ehrich Leonard

Proc. International Symposium on Nonlinear Theory and Its Applications (NOLTA), October 2005.
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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