Distributed Control Subject to Delays Satisfying an ${\mathcal{H}}_{\mathrm{\infty }}$ Norm Bound

This paper presents a characterization of distributed controllers subject to delay constraints induced by a strongly connected communication graph that achieve a prescribed closed loop ${\mathcal{H}}_{\mathrm{\infty }}$ norm. Inspired by the solution to the ${\mathcal{H}}_2$ problem subject to delays, we exploit the fact that the communication graph is strongly connected to decompose the controller into a local finite impulse response component and a global but delayed infinite impulse response component. This allows us to reduce the control synthesis problem to a linear matrix inequality feasibility test.