Diagnosing dynamical processes is a task with increasing importance in most industries. While machines grow in complexity, so do the requirements on their safety and productivity. Therefore, diagnostic methods are sought which accurately and automatically determine the presence and the type of faults occurring in a running process. This thesis presents a novel model-based diagnostic method which uses an explicit consideration of uncertainty, both in the model and in the measurements of the process. These uncertainties are assumed to be unknown-but-bounded, leading way to a set-theoretic diagnostic approach.The core of the diagnosis relies on a guaranteed state observation algorithm. Consequently, this thesis contains results in both the area of state observation and the area of fault diagnosis. Following the theoretic results, the method is illustrated using a simple example as well as a more advanced industrial case-study.