Directional interpolation via all-pass transfer function matrices and its application in Hankel-norm approximations

Shaked U.

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Directional interpolation via all-pass transfer function matrices and its application in Hankel-norm approximations

机译：通过全通传递函数矩阵的方向插值及其在Hankel范数逼近中的应用

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A new approach to the problem of multivariable interpolation via all-pass transfer function matrices that are not necessarily stable is presented. The approach applies to both state-space and classical function theoretic arguments and obtains a very simple expression for the all-pass matrix that satisfies the interpolation requirement. Unlike the solution that is obtained by the generalized Nevanlinna-Pick algorithm, this expression is derived in closed form explicitly in terms of the interpolation parameters. It allows a detailed investigation of the structure of the all-pass solution, and it is readily used in Hankel-norm approximations of linear multivariable systems.

机译：提出了一种通过不一定稳定的全通传递函数矩阵解决多变量插值问题的新方法。该方法适用于状态空间和经典函数理论参数，并获得满足插值要求的全通矩阵的非常简单的表达式。与通过广义的Nevanlinna-Pick算法获得的解决方案不同，该表达式根据插值参数以封闭形式显式导出。它允许详细研究全通解的结构，并且很容易用于线性多变量系统的Hankel范数逼近。

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《IEEE Transactions on Automatic Control》 |1990年第10期|P.1167-1170|共4页
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Shaked U.;
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Directional interpolation via all-pass transfer function matrices and its application in Hankel-norm approximations

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