The state equation

and the output equation

relate the finite-dimensional vectors

and w
n. The initial state x
0is known to belong to a set X
0and each w
n. to a set W
n, where

are compact and convex. Define

as the set of all possible values of x
ncompatible with observation of outputs

; it is compact and convex. S
nplays the same role as the a posteriori distribution in the stochastic case and is determined recursively by

and y
n. The sets involved are completely characterized by their support functions. The law of evolution of the support function of S
nis established. Some special cases and applications are pointed out.