The Deformed Consensus Protocol: Extended Version
For researchers in multi-agent systems, this work provides a theoretical extension of consensus protocols, but it is incremental as it analyzes a known variant without demonstrating practical advantages or performance gains.
This paper generalizes the continuous-time consensus protocol by replacing the Laplacian matrix with a deformed Laplacian, and studies its stability properties for various graph topologies using spectral theory of quadratic eigenvalue problems. Simulation results illustrate the theoretical findings.
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.