Hankel Singular Values and Vectors of a Class of Infinite-Dimensional Systems: Exact Hamiltonian Formulas for Control and Approximation Problems
Hankel Singular Values and Vectors of a Class of Infinite-Dimensional Systems: Exact Hamiltonian Formulas for Control and Approximation Problems
复制标题
一类无限维系统的汉克尔奇异值和向量：控制和逼近问题的精确哈密顿公式
DOI：
10.1007/pl00009857
复制
发表时间：
1999
期刊：
影响因子：
--
通讯作者：
Y. Ohta
中科院分区：
文献类型：
--
作者：
Y. Ohta
本文导出了符号为单输入单输出内函数与多输入多输出有理函数乘积的Hankel算子的奇异值和奇异向量的精确公式。这类Hankel算子源于具有有理权函数的灵敏度最小化H ∞控制问题和具有有理外部分的传递函数的逼近问题。证明了存在一个表征奇异值的Hamilton超越方程，从而导出了奇异向量的矩阵函数公式。
This paper derives exact formulas for singular values and vectors of Hankel operators whose symbol is a product of a single-input single-output inner function and a multi-input multi-output rational function. This class of Hankel operators arises from the sensitivity minimizationH∞control problem with a rational weight function and the approximation problem of transfer functions having rational outer parts. It is shown that there is a Hamiltonian transcendental equation characterizing singular values which leads to a matrix function formula for singular vectors.