Algebraic Characterizations of Consensus Problems for Networked Dynamic   Systems
  In this paper, we study the consensus problem for networked dynamic systems with arbitrary initial states, and present some structural characterization and direct construction of consensus functions. For the consensus problem under similar transformation, we establish some necessary and sufficient conditions by exploiting the structure of consensus functions. Finally, we discuss the consensus problem for dynamic systems under switching by using the common Lyapunov function method. 
Long Wang, Hong Shi, Feng Xiao