Positive edge consensus of networked systems with input saturation

This paper studies the edge consensus problems of undirected networked systems with positivity constraint and input saturation. Based on a given nodal network, the definition of edge network is introduced, and the edge dynamics is described by positive systems subject to input saturation. With the connections between the edge network and the nodal network, the lower and upper bounds of the nonzero eigenvalues of the edge Laplacian matrix are presented. Rigorous convergence analysis is carried out. Based on the special properties of positive systems, sufficient conditions of positive edge consensus with input saturation are given without using global topology information, that is, the topology information in the given results only relates to the edge and vertex number of the nodal network. Furthermore, the nonnegative edge consensus problem with uncertain parameters is also studied based on the properties of Metzler matrix. Different from many consensus problems with input saturation which achieve semi-global consensus, the results in this paper are global consensus. The feedback matrix can be computed by solving linear matrix inequality. Some illustrative numerical and practical simulation examples are finally introduced to verify the proposed methods in this paper.