论文标题
可控性椭圆形体积的分析表达和解构
Analytical Expression and Deconstruction of the Volume of the Controllability Ellipsoid
论文作者
论文摘要
在本文中，我们介绍了三个定理，并开发了一种有效的分析方法，以分析使用$ n $不同特征值的线性离散时间（LDT）系统的可控性椭圆形的体积。此外，通过解构体积的分析表达，椭圆形形状的某些因素，其限制的菱形的侧面长度，构建了LDT系统特征值分布的均匀性。基于体积和这些因素的分析表达，可以为LDT系统定义，计算，分析和优化控制能力。
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.
