Bipartite tracking consensus of generic linear agents with discrete-time dynamics over cooperation-competition networks

This article addresses the bipartite tracking consensus for a set of mobile autonomous agents over directed cooperation-competition networks. Here, cooperative and competitive interactions among the agents are described by positive and negative edges of the directed network topology, respectively. Both fixed and switching network topologies are considered. For the case with fixed network topology, the matrix product technique is utilized to derive the convergence result. For the case with switching network topologies, some key results related to the composition of binary relations are the main technical tools of analyzing the error system. In addition, the upper bound for the spectral radius of the system matrix is given to ensure the convergence of the system even if the single uncoupled system is strictly unstable. The applicability of the derived results is verified through two simulation experiments.