Seeking tracking consensus for general linear multiagent systems with fixed and switching signed networks

The existing studies for tracking consensus of multiagent systems (MASs) are all restricted to networks with only cooperative relationships among agents. Tracking consensus, however, requires beyond these traditional models due to the ubiquitous competition in many real-world MASs, such as biological systems and social systems. Taking into account this fact, this article aims to extend the dynamics of tracking consensus to signed networks containing both cooperative and competitive relationships among agents. A group of agents with general linear dynamics is considered. The cases of the fixed network as well as switching networks are analyzed, respectively. In the end, some algebraic conditions related to the network structure and the positive/negative edge weight are established to ensure the implementation of tracking consensus. Moreover, the single decoupling system is allowed to be strictly unstable in theory, and the upper bound of the eigenvalue modulus of the system matrix related to the system instability is given.