  It is well-known that linear quadratic regulators (LQR) enjoy guaranteed
stability margins, whereas linear quadratic Gaussian regulators (LQG) do not.
In this letter, we consider systems and compensators defined over directed
acyclic graphs. In particular, there are multiple decision-makers, each with
access to a different part of the global state. In this setting, the optimal
LQR compensator is dynamic, similar to classical LQG. We show that when
sub-controller input costs are decoupled (but there is possible coupling
between sub-controller state costs), the decentralized LQR compensator enjoys
similar guaranteed stability margins to classical LQR. However, these
guarantees disappear when cost coupling is introduced.
