The paper shows how proportional-integral-plus (PIP) control system design for rapidly sampled systems described by delta (δ) operator transfer function models is based on the formulation of a special non-minimum state space (NMSS) representation, whose state variables are the discrete-time derivatives of the output and input signals. The stochastic version of this model provides the basis for linear quadratic Gaussian (LQG) control system design in the δ domain. As in the more conventional minimum state space situation, the state variable feedback PIP control law is obtained straightforwardly by the introduction of a Kalman filter and the application of the separation principle. Although the resulting PIP control system is simple to implement, its exploitation of state variable feedback (SVF) ensures the power and flexibility of its operation.