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We analyze and design H-infinity controllers for general time-delay systemswith time-delays in systems' state, inputs and outputs. We allow the designerto choose the order of the controller and to introduce constant time-delays inthe controller. The closed-loop system of the plant and the controller ismodeled by a system of delay differential algebraic equations (DDAEs). Theadvantage of the DDAE modeling framework is that any interconnection of systemsand controllers prone to various types of delays can be dealt with in asystematic way, without using any elimination technique. We present apredictor-correct algorithm for the H-infinity norm computation of systemsdescribed by DDAEs. Instrumental to this we analyze the properties of theH-infinity norm. In particular, we illustrate that it may be sensitive withrespect to arbitrarily small delay perturbations. Due to this sensitivity, weintroduce the strong H-infinity norm which explicitly takes into account smalldelay perturbations, inevitable in any practical control application. Wepresent a numerical algorithm to compute the strong H-infinity norm for DDAEs.Using this algorithm and the computation of the gradient of the strongH-infinity norm with respect to the controller parameters, we minimize thestrong H-infinity norm of the closed-loop system based on non-smooth,non-convex optimization methods. By this approach, we tune the controllerparameters and design H-infinity controllers with a prescribed order orstructure.

Fixed-order H-infinity control for interconnected systems using delay differential algebraic equations