Direct Computing on Control Capability for Linear Continuous-time Systems Based on Hurwitz Matrix

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.