Functions of the Laplacian Matrix With Application to Distributed Formation Control

In this article, we study a class of matrix functions the combinatorial Laplacian that preserve its structure, i.e., define matrices, which are positive semidefinite and have zero row-sum nonpositive off-diagonal entries. This formulation has merit presenting different incarnations appeared in recent literature unified framework. For first time, apply family to consensus theory, show they leave agreement value unchanged offer distinctive advantages terms performance design flexibility. The theory is illustrated via worked examples numerical experiments featuring four representative shape-based distributed formation control strategy for single-integrator robots.