The standard adaptive optics (AO) system can be viewed as a sampled-data feedback system with a continuous-time disturbance (the incident wavefront from the observed object) and discrete-time measurement noise. A common measure of performance of AO systems is the time average of the pupil variance of the residual wavefront. This performance can be related to that of a discrete-time system obtained by lifting the incident and residual wavefronts. This article derives the corresponding discrete-time model and the computation of the AO system residual variance based on that model. The predicted variance of a single mode of an AO system is shown to be the same as that obtained via simulation.