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

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