  In this paper, based on the controllable canonical form and the Hurwitz
matrix of the Hurwitz stability criterion, an analytical volume computing
method for the smooth controllability zonotope for the linear
continuous-time(LCT) systems, without of help of the eigenvalue computing of
the systems, is presented. And then, the computing method is generlized to the
volume computing of the controllability ellipsoid of the LCT systems. Because
the controllability zonotope and ellipsoid are directly related to control
capability and their volumes are the main index describing the control
capability, the new volume computing methods proposed in this paper can help
greatly the computing, analysis and optimization of the control capability of
LCT systems.
