Right coprime factorisations using system upper Hessenberg forms-the multi-input system case

G.-R.Duan

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Right coprime factorisations using system upper Hessenberg forms-the multi-input system case

机译：使用系统上端Hessenberg进行正确的互质分解-多输入系统案例

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Based on a method for right coprime factorisation of linear systems using matrix elementary transformations, it is shown that a very simple iteration formula exists for right coprime factorisations of multi-input linear systems in system upper Hessenberg forms. This formula gives directly the coefficient matrices of the pair of solutions to the right coprime factorisation of the system Hessenberg form, and involves only inverses of a few triangular matrices and some matrix products and summations. Based on this formula, a simple, efficient procedure for determining a right coprime factoriation of a multi-input linear system is proposed, which first converts a given linear system into its system Hessenberg form using some orthogonal similarity transformations and then applies the iteration formula to the converted system Hessenberg form. An example demonstrates the use of the approach.

机译：基于使用矩阵基本变换的线性系统的右互质分解的方法，表明存在一个非常简单的迭代公式，用于系统上Hessenberg形式的多输入线性系统的右互质分解。该公式直接给出了系统Hessenberg形式的正确互质分解的解对的系数矩阵，并且仅涉及几个三角形矩阵的逆矩阵以及一些矩阵乘积和总和。基于该公式，提出了一种简单有效的确定多输入线性系统的右互素分解的程序，该程序首先使用一些正交相似变换将给定的线性系统转换为系统Hessenberg形式，然后将迭代公式应用于转换后的系统为Hessenberg形式。一个示例演示了该方法的使用。

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《IEE Proceedings. Part D》 |2001年第6期|p.433-441|共9页
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G.-R.Duan;
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正文语种 eng
中图分类电气化、电能应用;
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Right coprime factorisations using system upper Hessenberg forms-the multi-input system case

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