  This paper studies a generalization of the standard continuous-time consensus
protocol, obtained by replacing the Laplacian matrix of the communication graph
with the so-called deformed Laplacian. The deformed Laplacian is a
second-degree matrix polynomial in the real variable 's' which reduces to the
standard Laplacian for 's' equal to unity. The stability properties of the
ensuing deformed consensus protocol are studied in terms of parameter 's' for
some special families of undirected and directed graphs, and for arbitrary
graph topologies by leveraging the spectral theory of quadratic eigenvalue
problems. Examples and simulation results are provided to illustrate our
theoretical findings.
