Two common ways to design a digital system are

1. to do analog design and approximate by a digital implementation;​
2. to approximate the plant by its discretization and do a discrete-time design.

The main disadvantage of the first is that performance recovery normally occurs when the sampling period tends to zero;​ the second has the disadvantage of ignoring intersample behavior.

The approach in this thesis is to study linear sampled-data systems as time-varying systems operating in continuous time and design directly with the true performance specs expressed in terms of continuous signals. Topics investigated include basic properties of the sampling operator, internal stability of sampled-data systems, and optimal sampled-data design with an ℋ₂ or ℋ_∞ performance criterion. In many cases we show how a sampled-data problem can be recast as a discrete-time problem and hence be solved via known techniques. The main mathematical tool used is operator theory.