Chained aggregation has been introduced as a procedure for transforming a system into the generalized Hessenberg representation (GHR). A three-control-component design (TCCD) based on the GHR for hierarchical control of large scale systems has been proposed. Here, a geometric analysis of the GHR is given, and the underlying features of the TCCD are exposed. This allows the development of a more general version of the TCCD, and a deeper understanding of the structural features of the resulting design. A key idea, model reduction by residual system feedback, is explored extensively.