Formulation and analysis of stability for spacecraft formations

A formulation of stability for formation flying spacecraft is presented. First, a formation is defined via control interactions between the spacecraft. Then, stability is formulated on the basis of input-to-output stability with respect to a partitioning of the formation dynamics. The particular form of input-to-output stability used here is based on the peak-to-peak gain of a system from its input to its output. This formulation of stability is shown to be useful in characterising disturbance propagation in the formation as a function of the partition interconnection topology, and also in analysing the robustness of sensing, communication and control topologies. Stability analysis results are presented for hierarchical, cyclic and disturbance attenuating formations in terms of the input-to-output gains of the partitions in the formation. Finally, Lyapunov stability analysis results are provided in terms of linear matrix inequalities for a general class of formations.