Summary
International Symposium on Nonlinear Theory and its Applications
2005
Session Number:3-1-1
Session:
Number:3-1-1-2
Graph Laplacian and Lyapunov design of collective planar motions
Rodolphe Sepulchre, Derek Paley, Naomi Ehrich Leonard,
pp.679-682
Publication Date:2005/10/18
Online ISSN:2188-5079
Summary:
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.