FINITE TIME STABILITY AND RELATIVE CONTROLLABILITYOF SECOND ORDER LINEAR DIFFERENTIAL SYSTEMSWITH PURE DELAY

被引：1

作者：

Li, Mengmeng ^{[1
]}

Feckan, Michal ^{[2
,3
]}

Wang, JinRong ^{[1
]}

机构：

[1] Guizhou Univ, Dept Math, Guiyang 550025, Guizhou, Peoples R China

[2] Comenius Univ, Dept Math Anal & Numer Math, Fac Math Phys & Informat, Bratislava 84248, Slovakia

[3] Slovak Acad Sci, Math Inst, Stefanikova 49, Bratislava 81473, Slovakia

来源：

APPLICATIONS OF MATHEMATICS | 2023年 / 68卷 / 03期

基金：

中国国家自然科学基金;

关键词：

finite time stability; relative controllability; second order; delayed matrix function; SOBOLEV TYPE; REPRESENTATION; EQUATIONS;

D O I：

10.21136/AM.2022.0249-21

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We first consider the finite time stability of second order linear differential systems with pure delay via giving a number of properties of delayed matrix functions. We secondly give sufficient and necessary conditions to examine that a linear delay system is relatively controllable. Further, we apply the fixed-point theorem to derive a relatively controllable result for a semilinear system. Finally, some examples are presented to illustrate the validity of the main theorems.

引用

页码：305 / 327

页数：23

共 20 条

[1] ON THE NEW CONTROL FUNCTIONS FOR LINEAR DISCRETE DELAY SYSTEMS [J].

Diblik, J. ;

Feckan, M. ;

Pospisil, M. .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2014, 52 (03) :1745-1760

[2] Representation of a solution of the Cauchy problem for an oscillating system with two delays and permutable matrices [J].

Diblik, J. ;

Feckan, M. ;

Pospisil, M. .

UKRAINIAN MATHEMATICAL JOURNAL, 2013, 65 (01) :64-76

[3] Controllability of linear discrete systems with constant coefficients and pure delay [J].

Diblik, Josef ;

Khusainov, Denys Ya. ;

Ruzickova, M. .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2008, 47 (03) :1140-1149

[4] Representation of solutions of linear differential systems with pure delay and multiple delays with linear parts given by non-permutable matrices [J].

Elshenhab, Ahmed M. ;

Wang, Xing Tao .

APPLIED MATHEMATICS AND COMPUTATION, 2021, 410

[5] Controllability of Fractional Functional Evolution Equations of Sobolev Type via Characteristic Solution Operators [J].

Feckan, Michal ;

Wang, JinRong ;

Zhou, Yong .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2013, 156 (01) :79-95

[6]

Gantmakher F. R., 1967, The Theory of Matrices

[7] REPRESENTATION OF A SOLUTION OF THE CAUCHY PROBLEM FOR AN OSCILLATING SYSTEM WITH PURE DELAY [J].

Khusainov, D. Ya. ;

Diblik, J. ;

Ruzickova, M. ;

Lukacova, J. .

NONLINEAR OSCILLATIONS, 2008, 11 (02) :276-285

[8] Relative controllability in systems with pure delay [J].

Khusainov, DY ;

Shuklin, GV .

INTERNATIONAL APPLIED MECHANICS, 2005, 41 (02) :210-221

[9] Finite-time stability analysis of fractional order time-delay systems: Gronwall's approach [J].

Lazarevic, Mihailo P. ;

Spasic, Aleksandar M. .

MATHEMATICAL AND COMPUTER MODELLING, 2009, 49 (3-4) :475-481

[10] Exploring delayed Mittag-Leffler type matrix functions to study finite time stability of fractional delay differential equations [J].

Li, Mengmeng ;

Wang, JinRong .

APPLIED MATHEMATICS AND COMPUTATION, 2018, 324 :254-265

← 1 2 →