2020/04/12 by Mingwang Zhao, Zhao, Mingwang · 1 citation
Engineering · Mathematics · #Control and Stability of Dynamical Systems #FOS: Electrical engineering #FOS: Mathematics #Numerical methods for differential equations #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2004.05528
openalex publication_date 2020/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.