  In this article, we define a class of special zonotopes generated by a matrix
pair with finite-interval parameters. We discuss the relationship between the
volume of these zonotopes and the controllability of one aspect (the volume of
the controllable region) of the dynamic systems. We present a corollary and
develop an effective recursive method to compute the volume of the special
zonotopes. Furthermore, we develop two recursive and analytical
volume-computation methods for the finite- and infinite-time controllable
regions with real eigenvalues. We conduct numerical experiments to demonstrate
the effectiveness of these new volume-computation methods for zonotopes and
regions.
