Distributed Bipartite Containment Tracking over Signed Networks with Multiple Leaders

We address the distributed bipartite containment tracking-control problem for second-order systems over multi-leader signed networks. In such systems, the networks' interconnections have signed weights; they are positive if the agents are cooperative with each other and negative otherwise. Moreover, as multiple leaders intervene in the network, it is hardly possible to achieve consensus, unless very stringent conditions are met. Instead, all the agents' states converge to a residual compact set resulting from the agents' initial conditions and the network's topology. In this paper, we propose a bipartite-containment controller for second-order linear systems. For the containment set we establish global exponential (hence, robust) stability, and we compute the specific equilibria to which all agents converge inside the containment set. In addition, we provide strict Lyapunov functions for signed-graph networks. Also, we illustrate our theoretical findings via numerical simulations.