AbstractThis paper gives a concise description of effective solutions to the guaranteed state estimation problems for dynamic systems with uncertain items being unknown but bounded. It indicates a rather unconventional, rigorous theory for these problems based on the notion of evolution equations of the ‘funnel’ type which could be further transformed ‐ throughexactellipsoidal representations ‐ into algorithmic procedures that allow effective simulation, particularly with computer graphics. the estimation problem is also interpreted as a problem of tracking a partially known system under incomplete measurements.Mathematically, the technique described in this paper is based on a theory of set‐valued evolution equations with the approximation of solutions formulated in terms of set‐valued calculus by ellipsoidal‐val