Topological equivalence of linear time-varying control systems

被引：0

作者：

Li, Jing ^{[1
]}

Zhang, Zhixiong ^{[2
]}

机构：

[1] Southwestern Univ Finance & Econ, Sch Math, Chengdu 611130, Peoples R China

[2] Sichuan Univ, Sch Math, Chengdu 610064, Peoples R China

来源：

IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION | 2023年 / 40卷 / 02期

基金：

中国国家自然科学基金;

关键词：

linear time-varying control systems; classification; topological equivalence; linear equivalence; Krylov indices; CLASSIFICATION; LINEARIZATION;

D O I：

10.1093/imamci/dnad009

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, we mainly studied the topological equivalence of linear time-varying (LTV) control system x? (t) = A(t)x(t) + B(t)u(t) defined on an interval I ? 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.

引用

页码：253 / 284

页数：32

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