可控椭球体积的解析表示与解构
Analytical Expression and Deconstruction of the Volume of the Controllability Ellipsoid
摘要：
本文给出了$n$不同特征值的线性离散系统能控性椭球体积的三个定理，并给出了一种有效的解析计算方法.进而，通过对体积解析表达式的解构，构造了影响LDT系统特征值分布均匀性的椭球形状、外接菱形边长等因素。基于体积和这些因素的解析表达式，可以定义、计算、分析和优化LDT系统的控制能力。
英文摘要：
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.
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