On the Stability and Null-Controllability of an Infinite System of Linear Differential Equations

被引：5

作者：

Azamov, Abdulla ^{[1
]}

Ibragimov, Gafurjan ^{[2
,3
]}

Mamayusupov, Khudoyor ^{[4
,5
]}

Ruziboev, Marks ^{[6
]}

机构：

[1] Uzbek Acad Sci, VI Romanovskiy Inst Math, Sect Dynam Syst & Their Applicat, 4 Univ St, Tashkent 100174, Uzbekistan

[2] Univ Putra Malaysia, Dept Math, Seri Kembangan, Malaysia

[3] Univ Putra Malaysia, Inst Math Res, Seri Kembangan, Malaysia

[4] Moscow Inst Phys & Technol, Inst Lane 9, Dolgoprudnyi 141700, Moscow Region, Russia

[5] Natl Univ Uzbekistan, 4 Univ St, Tashkent 100174, Uzbekistan

[6] Univ Vienna, Fac Math, Oskar Morgnstern Pl 1, Vienna, Austria

来源：

JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS | 2023年 / 29卷 / 03期

关键词：

Differential equations in Banach spaces; Stability; Controllable system; Gramian operators; Eigenvalues; TIME; GAME;

D O I：

10.1007/s10883-021-09587-6

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 work, the null controllability problem for a linear system in l(2) is considered, where the matrix of a linear operator describing the system is an infinite matrix with lambda is an element of R on the main diagonal and is above it. We show that the system is asymptotically stable if and only if lambda <= -1, which shows the fine difference between the finite and the infinite-dimensional systems. When lambda <= -1 we also show that the system is null controllable in large. Further we show a dependence of the stability on the norm, i.e. the same system considered l(infinity) is not asymptotically stable if lambda = -1.

引用

页码：595 / 605

页数：11

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