This text gives an account of an ellipsoidal calculus and ellipsoidal techniques that allows presentation of the set-valued solutions to these problems in terms of approximating ellipsoidal-valued functions. Such an approach leads to effective computation schemes, an dopens the way to applications and implementations with computer animation, particularly in decision support systems. The problems treated here are those that involve calculation of attainability domains, of control synthesis under bounded controls, state constraints and unknown input disturbances, as well as those of "viability" and of the "bounding approach" to state estimation. The text ranges from a specially developed theory of exact set-valued solutions to the description of ellipsoidal calculus, related ellipsoidal-based methods and examples worked out with computer graphics. the calculus given here may also be interpreted as a generalized technique of the "interval analysis" type with an impact on scientific computation.