Laplacian transformation for average consensus of directed multi-agent networks

Network consensus algorithms have extensive applications in coordination of robot groups and decision making of agents. Among consensus algorithms, the so-called average consensus is important for its wide application in signal processing problems. In this paper, we discuss the Laplacian dynamic for average consensus problems. Motivated by the observation of the relationship between the weight balance problem and the underlying Markov chain, we have proposed an approach to transform general Laplacian matrices to those associated with balanced digraphs. As a result, with the transformed Laplacian dynamics, multi-agent systems can asymptotically achieve average consensus. We also provide a computation approach to simplify the procedures of obtaining the transformation result. Finally, a numerical example is presented to illustrate the proposed approach.