Necessary and sufficient conditions for assignability of dichotomy spectra of continuous time-varying linear systems

被引：6

作者：

Babiarz, Artur ^{[1
]}

Le Viet Cuong ^{[2
]}

Czornik, Adam ^{[1
]}

Thai Son Doan ^{[3
]}

机构：

[1] Silesian Tech Univ, Dept Automat Control & Robot, Gliwice, Poland

[2] Natl Univ Civil Engn, Dept Informat Technol, Hanoi, Vietnam

[3] Vietnam Acad Sci & Technol, Inst Math, Hanoi, Vietnam

来源：

AUTOMATICA | 2021年 / 125卷

关键词：

Dichotomy spectrum; Continuous time-varying linear systems; Controllability; Assignability; DIFFERENTIAL-EQUATIONS; LYAPUNOV;

D O I：

10.1016/j.automatica.2020.109466

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We consider a version of the pole placement problem for continuous time-varying linear systems. Our purpose is to prove that uniform complete controllability is equivalent to possibility of arbitrary assignment of the dichotomy spectrum. The main ingredients of the proof are the reduction of system to upper triangular form and the use of the concept of uniform complete stabilization. To illustrate the theoretical result, we consider scalar continuous time-varying control systems. For these systems we provide a simple necessary and sufficient condition for uniform complete controllability and if this condition holds, then we construct an explicit control to assign the dichotomy spectrum. (C) 2020 Elsevier Ltd. All rights reserved.

引用

页数：8

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