Conic-Sector-Based Control in the Presence of Delay∗

Linear matrix inequality conditions implying interior conic bounds are developed for stable linear time-invariant systems with unknown input delay. Combined with the Conic Sector Theorem, these bounds enable the design of controllers ensuring closed-loop input-output stability that is robust with respect to input delay uncertainty. These contributions are used in a numerical example to design a nearly-optimal controller, which, for moderate delays, achieves improved performance relative to an H2–optimal controller designed for the nominally undelayed system. Moreover, the nearly-optimal controller has guaranteed input-output-stability for all delays, while in simulation the H2–optimal controller is observed to destabilize the closed-loop when adequately large delays are present.