Improved results on distributed observer-based positive edge consensus

Abstract

This paper revisits the observer-based positive edge consensus problem for nodal networks. So far, existing positive edge consensus of directed networks with less conservative connectivity conditions have to use the global topology information. On the other hand, instead of using global topology information, the positive consensus conditions using the bounds of the eigenvalues of the Laplacian matrix are conservative. To tackle these problems, less conservative bounds of the eigenvalues of the Laplacian matrix are presented. Based on a general distributed observer-based approach, the necessary and sufficient conditions of the edge consensus are derived. And then, with the improved bounds of the Laplacian eigenvalues, less conservative sufficient conditions without using global topology information are given. By solving the algebraic Riccati inequalities, semi-definite programming algorithms are developed to obtain the solutions. Finally, simulation results are also given to illustrate the given results.