带封闭反馈的线性控制系统的频谱分配问题解决方案

IF 0.8 4区数学 Q2 MATHEMATICS

Differential Equations 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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来源期刊

Differential Equations 数学-数学

CiteScore

1.30

自引率

33.30%

发文量

审稿时长

3-8 weeks

期刊介绍： Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.