Topological equivalence of linear time-varying control systems

IF 1.6 4区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

IMA Journal of Mathematical Control and Information Pub Date : 2023-04-21 DOI:10.1093/imamci/dnad009

Jing Li, Zhixiong Zhang

引用次数: 0

Abstract

In this paper, we mainly studied the topological equivalence of linear time-varying (LTV) control system $\dot{x}\left ( t\right )=A(t)x(t)+B(t)u(t)$ defined on an interval $I \subset \mathbb{R}^{+}$. After giving a new definition of the topological equivalence, we investigated the local equivalence of LTV control systems under two new hypotheses. These hypotheses were made by the local behavior of Krylov indices (which turned out to be controllability indices for the linear time-invariant (LTI) control systems). It was found out that Krylov indices play an important role in the classification problem of LTV control systems. Compared with our former work on the topological equivalence of LTI control systems, new methods and techniques were taken to deal with new difficulties occurred for LTV control systems.

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线性时变控制系统的拓扑等价性

本文主要研究在区间$I \subset \mathbb{R}^{+}$上定义的线性时变(LTV)控制系统$\dot{x}\left ( t\right )=A(t)x(t)+B(t)u(t)$的拓扑等价性。在给出拓扑等价的新定义后，研究了LTV控制系统在两个新假设下的局部等价性。这些假设是由Krylov指数的局部行为提出的(Krylov指数是线性时不变(LTI)控制系统的可控性指标)。研究发现，Krylov指数在LTV控制系统的分类问题中起着重要的作用。与以往LTI控制系统拓扑等价的研究相比，本文采用了新的方法和技术来解决LTV控制系统出现的新问题。

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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来源期刊

IMA Journal of Mathematical Control and Information 工程技术-应用数学

CiteScore

3.30

自引率

6.70%

发文量

审稿时长

>12 weeks

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