Pairwise synchronization of second-order matrix-weighted networks

Abstract This paper deals with the pairwise synchronization of second-order linear time invariant (LTI) systems with incommensurable outputs through a matrix-weighted graph. The pairwise synchronization here means that the relative outputs have pairwise synchronized solutions for the identical LTI systems. For the matrix-weighted network, some necessary and sufficient conditions on the pairwise synchronization are given by means of the Jordan form, matrix decomposition and effective conductance. Moreover, the relationship between the global synchronization and the connectivity of its interconnection graph is also discussed. Examples and simulations are shown to verify the theoretical results.