Passivity as a design tool for group coordination

We pursue a group coordination problem where the objective is to steer the differences between output variables of the group members to a prescribed compact set via distributed feedback rules. When the information flow between neighboring members is bidirectional, we show that the closed-loop system exhibits a special interconnection structure which inherits the passivity properties of its components. By exploiting this structure we develop a passivity-based design framework, which results in a broad class of feedback rules that encompass as special cases some of the existing formation stabilization and group agreement designs in the literature. The passivity approach offers additional design flexibility compared to these special cases, and systematically constructs a Lurie-type Lyapunov function for the closed-loop system. We further study the robustness of the feedback laws in the presence of a time-varying communication topology