The propagation of parametric uncertainty via polytopes

We consider the discrete dynamical system
x(k+1)= A(k)x(k)
with n
²
independently varying uncertainties in the entries of
A (\cdot)
. Although the set of possible states
X(k)
at time
k
is not necessarily convex, we show that the convex hull of this set can be recursively propagated forward in time.