Summary: We analyze and design \(H_{\infty}\) controllers for general time-delay systems with time-delays in systems’ state, inputs, and outputs. We allow the designer to choose the order of the controller and to introduce constant time-delays into the controller. The closed-loop system of the plant and the controller is modeled by a system of Delay Differential Algebraic Equations (DDAEs). The advantage of the DDAE modeling framework is that any interconnection of systems and controllers prone to various types of delays can be dealt with in a systematic way, without using any elimination technique. We present a predictor-corrector algorithm for the \(H_{\infty}\) norm computation of systems described by DDAEs. Instrumental to this we analyze the properties of the \(H_{\infty}\) norm. In particular, we illustrate that it may be sensitive with respect to arbitrarily small delay perturbations. Due to this sensitivity, we introduce the strong \(H_{\infty}\) norm, which explicitly takes into account small delay perturbations, inevitable in any practical control application. We present a numerical algorithm to compute the strong \(H_{\infty}\) norm for DDAEs. Using this algorithm and the computation of the gradient of the strong \(H_{\infty}\) with respect to the controller parameters, we minimize the strong \(H_{\infty}\) norm of the closed-loop system based on nonsmooth, nonconvex optimization methods. By this approach, we tune the controller parameters and design \(H_{\infty}\) controllers with a prescribed order or structure.