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. To stabilize this set we study a class of feedback rules that are implementable with local information available to each member. 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 these feedback laws in the presence of a time-varying communication topology, and present a persistency of excitation condition which allows the interconnection graph to lose connectivity pointwise in time as long as it is established in an integral sense.