  In this article, we present three theorems and develop an effective
analytical method to compute analytically the volume of the controllability
ellipsoid for the linear discrete-time (LDT) systems with $n$ different
eigenvalues. Furthermore, by deconstructing the analytical expression of the
volume, some factors on the shape of the ellipsoid, the side length of its
circumscribed rhomboid, the evenness of the eigenvalue distribution of the LDT
system are constructed. Based on the analytical expression of the volume and
these factors, the control ability can be defined, computing, analyzed, and
optimized for the LDT systems.
