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

TL;DR

This paper introduces an analytical method to compute the volume of controllability regions for linear continuous-time systems using the Hurwitz matrix, avoiding eigenvalue calculations, thus aiding control capability analysis.

Contribution

It presents a novel volume computation approach based on the Hurwitz matrix for controllability regions, enhancing analysis and optimization of control capability without eigenvalue computation.

Findings

Analytical volume computation method for controllability zonotope.

Extension of the method to controllability ellipsoid.

Facilitates control capability analysis and optimization.

Abstract

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.