One of the main concerns in the design of networked control systems (NCS's) is the inherent delays induced by the networking infrastructure. Rather than considering delays as a threat, delays may be considered as an opportunity for novel controller design procedures, where delays become a design parameter. The benefits may range from easier and cheaper implementations to improved performance. To enable procedures where the explicit specification of a delay may be profitable, alternative models for a discrete-time LTI system with an arbitrary delay used for controller design must be investigated. This paper presents a modeling effort different than the common approach of extending the state-space model with new state variables. The new model is also capable of representing the same system with a delay but using a state-space modeling structure that keeps the original system order. The focus of the paper is to show that both models are equivalent. A direct consequence is that it will be possible to design a controller for a system without delay in such a way that the closed loop system behaves like having a delay. In other words, a relation between desired control performance (via e.g. closed-loop system poles), controller, and delay is established, which provides a new design criterion for NCS.