带封闭反馈的线性控制系统的频谱分配问题解决方案

Pub Date : 2024-09-19 DOI:10.1134/s0012266124060065

S. P. Zubova, E. V. Raetskaya

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引用次数: 0

摘要

摘要本文给出了一种构建反馈矩阵以解决线性动力系统频谱分配（频谱控制；极点分配）问题的方法。在级联分解法的构建过程中，形成了关于动态系统完全可控性与反馈矩阵存在性之间联系的著名定理的新证明。确定了影响矩阵非唯一性的全部任意元素集合。给出了在实谱和存在复共轭特征值以及多特征值情况下构建反馈矩阵的示例。在反馈矩阵固定的情况下，研究了指定频谱在系统参数微小扰动下的稳定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Solution of the Spectrum Allocation Problem for a Linear Control System with Closed Feedback

Abstract

A method for constructing a feedback matrix to solve the spectrum allocation (spectrum control; pole assignment) problem for a linear dynamical system is given. A new proof of the well-known theorem about the connection between the complete controllability of a dynamical system and the existence of a feedback matrix is formed in the process of constructing the cascade decomposition method. The entire set of arbitrary elements affecting the nonuniqueness of the matrix is identified. Examples of constructing a feedback matrix in the case of a real spectrum and in the presence of complex conjugate eigenvalues as well as for the case of multiple eigenvalues are given. The stability of the specified spectrum under small perturbations of system parameters with a fixed feedback matrix is studied.

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