h-Stability of set differential equations

被引：0

作者：

Boukthir, Sihem ^{[1
,2
]}

Ghanmi, Boulbaba ^{[3
]}

Basdouri, Imed ^{[3
]}

Ichalal, Dalil ^{[2
]}

Lerbet, Jean ^{[4
]}

机构：

[1] Fac Sci Sfax, Dept Math, Route Soukra Km 4, BP 802, Sfax 3018, Tunisia

[2] Univ Paris Saclay Univ, Univ Evry Val Essonne, IBISC Lab, 40 Rue Pelvoux, F-91020 Evry Courcouronnes, France

[3] Fac Sci Gafsa, Dept Math, Gafsa 2112, Tunisia

[4] Univ Paris Saclay, Univ Evry Val Essonne, Lamme Lab, CNRS,UMR 8071, 23 Bd France, F-91037 Evry, France

来源：

ARCHIVES OF CONTROL SCIENCES | 2023年 / 33卷 / 04期

关键词：

h-stability; Lyapunov theory; set-valued differential; generalized Hukuhara derivative; perturbed system; cascaded systems; NONLINEAR-SYSTEMS; THEOREMS; INTERVAL;

D O I：

10.24425/acs.2023.148880

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 introduce the notion of h-stability for set-valued differential equations. Necessary and sufficient conditions are established by using Lyapunov theory. Then, based on the obtained results, we study the h-stability of perturbed and cascaded systems. Finally, an example illustrates the proposed theorems.

引用

页码：761 / 788

页数：28

共 37 条

[1] PERTURBATION THEOREMS FOR NON-LINEAR SYSTEMS OF ORDINARY DIFFERENTIAL-EQUATIONS
ATHANASSOV, ZS
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1982, 86 (01) : 194 - 207
[2] Aubin JP, 2009, Set-valued analysis, DOI 10.1007/978-0-8176-4848-0
[3] Nonlinear variation of parameters formula for set differential equations in a metric space
Bhaskar, TG
Lakshmikantham, V
Devi, JV
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 63 (5-7) : 735 - 744
[4] Uniform global practical asymptotic stability for time-varying cascaded systems
Chaillet, Antoine
Loria, Antonio
[J]. EUROPEAN JOURNAL OF CONTROL, 2006, 12 (06) : 595 - 605
[5] CHoI S.K., 1997, Dynamic Systems and Applications, V6, P397
[6] Choi S.K., 1997, B KOREAN MATH SOC, V34, P371
[7] Variationally stable difference systems by n∞-similarity
Choi, SK
Koo, NJ
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2000, 249 (02) : 553 - 568
[8] h-stability of dynamic equations on time scales with nonregressivity
Choi, Sung Kyu
Goo, Yoon Hoe
Koo, Namjip
[J]. ABSTRACT AND APPLIED ANALYSIS, 2008,
[9] New converse Lyapunov theorems and related results on exponential stability
Corless, M
Glielmo, L
[J]. MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 1998, 11 (01) : 79 - 100
[10] De Blasi F.S., 1969, Boll. Unione Mat. Ital., V4, P491

← 1 2 3 4 →