A decomposition approach to distributed control of spatially invariant systems

This note considers the decentralized control of spatially invariant systems, i.e., systems of homogeneous interacting components. The main idea is for individual components to model interactions with neighbors as disturbances that satisfy certain magnitude bounds while simultaneously self-imposing symmetric magnitude bounds. These magnitude bounds can be interpreted as negotiated levels of interaction among components. It turns out that this approach is equivalent to constructing a feedback that is robustly stabilizing with structured uncertainties.