Distributed Bipartite Containment Tracking over Signed Networks with Multiple Leaders

Submitted for publication in IEEE Trans. Control of Network SystemsWe address the distributed bipartite containment tracking-control problem for second-order systems steered by multiple cooperative and antagonistic leaders. The influence of the former is represented via positive links, while negative interconnections are used for the latter, thereby generating a signed network. Because of the presence of diverse leaders, having positive or negative influence on the followers, complete consensus is impossible. Instead, the followers' respective states may only converge to a residual compact set, not predefined, but resulting from the agents' initial conditions and the network's topology. For this set, which is called bipartite containment set, we establish global exponential stability and we compute the specific equilibria to which all agents converge inside the containment set (this is called multiconsensus). In addition, we provide strict Lyapunov functions for signed-graph networks and establish robustness of the bipartite containment tracking control. Finally, we illustrate our theoretical findings via numerical simulations