Fixed-order strong H-infinity control of interconnected systems with time-delays

We design fixed-order strong H-infinity controllers for general time-delay systems. The designer chooses the controller order and may introduce constant time-delays in the controller. We represent the closed-loop system of the plant and the controller as delay differential algebraic equations (DDAEs). This representation deals with any interconnection of systems with time-delays without any elimination techniques. We present a numerical algorithm to compute the strong H-infinity norm for DDAEs which is robust to arbitrarily small delay perturbations, unlike the standard H-infinity norm. We optimize the strong H-infinity norm of the closed-loop system based on non-smooth, non-convex optimization methods using this algorithm and the computation of the gradient of the strong H-infinity norm with respect to the controller parameters. We tune the controller parameters and design H-infinity controllers with a prescribed order or structure.