论文标题
由矩阵对生成的精确量
Exact Volume of Zonotopes Generated by a Matrix Pair
论文作者
论文摘要
在本文中，我们定义了由带有有限间隔参数的矩阵对生成的一类特殊界限。我们讨论了这些地位的体积与动态系统的一个方面（可控区域的体积）的可控性之间的关系。我们提出了一种推论，并开发了一种有效的递归方法来计算特殊地位的体积。此外，我们为具有实际特征值的有限时间和无限时间可控区域开发了两种递归和分析量的计算方法。我们进行数值实验，以证明这些新的体积计算方法对地位和区域的有效性。
In this article, we define a class of special zonotopes generated by a matrix pair with finite-interval parameters. We discuss the relationship between the volume of these zonotopes and the controllability of one aspect (the volume of the controllable region) of the dynamic systems. We present a corollary and develop an effective recursive method to compute the volume of the special zonotopes. Furthermore, we develop two recursive and analytical volume-computation methods for the finite- and infinite-time controllable regions with real eigenvalues. We conduct numerical experiments to demonstrate the effectiveness of these new volume-computation methods for zonotopes and regions.
