Existence and Generic Properties of L2 Approximants for Linear Systems
Existence and Generic Properties of L2 Approximants for Linear Systems
复制标题
线性系统L2近似的存在性和泛性
DOI：
10.1093/imamci/3.2-3.89
复制
发表时间：
1986
影响因子：
1.5
通讯作者：
L. Baratchart
中科院分区：
文献类型：
--
作者：
L. Baratchart
本文研究的问题是一个（可能是非理性的）给定的稳定的离散系统的最佳逼近的有限维之一，其中的约束的尺寸的逼近。该准则是传递函数的L2范数。在本文中，我们感兴趣的只是一般的定性性质的集合的逼近。我们首先展示存在性。然后，我们证明，例如，最佳逼近几乎总是循环的，有限的数量。
The problem examined in this paper is the best approximation of a (possibly non-rational) given stable discrete system by a finite-dimensional one, where a bound on the dimension of the approximant is imposed. The criterion is the L2norm of the transfer function. In this paper, we are interested only in generic qualitative properties of the set of approximants. We first show eixstence. We then prove, for instance, that best approximants are almost always cyclic, and finite in number.