On the Practical h-stability of Nonlinear Systems of Differential Equations

被引：16

作者：

Ghanmi, B. ^{[1
,2
]}

机构：

[1] Univ Gafsa, Gafsa, Tunisia

[2] Fac Sci Gafsa, Dept Math, Sidi Ahmed Zarroug 2112, Gafsa, Tunisia

来源：

JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS | 2019年 / 25卷 / 04期

关键词：

h-stability; Practical h-stability; Lyapunov theory; Perturbed systems; Cascaded systems; Practical h-stabilization;

D O I：

10.1007/s10883-019-09454-5

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 present a new notion of stability for nonlinear systems of differential equations called practical h-stability. Necessary and sufficient conditions for practical h-stability are given using the Lyapunov theory. Our original results generalize well-known fundamental results: practical exponential stability, practical asymptotic stability, and practical stability for nonlinear time-varying systems. In addition, these results are used to study the practical h-stability of two important classes of nonlinear systems, namely perturbed and cascaded systems. The last part is devoted to the study of the problem of practical h-stabilization for certain classes of nonlinear systems.

引用

页码：691 / 713

页数：23

共 50 条

[41] Stability of nonlinear asynchronous systems [J].

de la Pena, David Munoz ;

Christofides, Panagiotis D. .

SYSTEMS & CONTROL LETTERS, 2008, 57 (06) :465-473

[42] On practical h-observer design for nonlinear non-autonomous dynamical systems with disturbances [J].

Alaya, Manel ;

Damak, Hanen ;

Taieb, Nizar Hadj ;

Hammami, Mohamed Ali .

ARCHIVES OF CONTROL SCIENCES, 2024, 34 (04) :881-895

[43] BOUNDEDNESS IN THE NONLINEAR FUNCTIONAL DIFFERENTIAL SYSTEMS [J].

Choi, Sang Il ;

Goo, Yoon Hoe .

COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, 2015, 30 (04) :415-427

[44] ON PRACTICAL STABILITY OF TIME SCALE PERTURBED SYSTEMS [J].

Ben Nasser, Bacem ;

Hammami, Mohamed Ali .

JOURNAL OF DYNAMICAL SYSTEMS AND GEOMETRIC THEORIES, 2014, 12 (01) :51-67

[45] H∞ Chaos Synchronization for Nonlinear Bloch Equations [J].

Ahn, Choon Ki .

JOURNAL OF THE KOREAN PHYSICAL SOCIETY, 2009, 55 (06) :L2295-L2300

[46] Some New Results on Stability and Input to State Stability of Fuzzy Differential Equations [J].

Ghanmi, Boulbaba ;

Mnasri, Ichrak .

ANNALS OF THE UNIVERSITY OF CRAIOVA-MATHEMATICS AND COMPUTER SCIENCE SERIES, 2024, 51 (02) :430-448

[47] BOUNDEDNESS IN THE FUNCTIONAL NONLINEAR PERTURBED DIFFERENTIAL SYSTEMS [J].

Goo, Yoon Hoe .

JOURNAL OF THE KOREAN SOCIETY OF MATHEMATICAL EDUCATION SERIES B-PURE AND APPLIED MATHEMATICS, 2015, 22 (02) :101-112

[48] On the practical h-stabilization of nonlinear time-varying systems: application to separately excited DC motor [J].

Damak, Hanen ;

Hammami, Mohamed Ali ;

Kicha, Abir .

COMPEL-THE INTERNATIONAL JOURNAL FOR COMPUTATION AND MATHEMATICS IN ELECTRICAL AND ELECTRONIC ENGINEERING, 2021, 40 (04) :888-904

[49] On global uniform asymptotic stability of nonlinear time-varying systems in cascade [J].

Panteley, E ;

Loria, A .

SYSTEMS & CONTROL LETTERS, 1998, 33 (02) :131-138

[50] PRACTICAL EXPONENTIAL STABILITY OF PERTURBED TRIANGULAR SYSTEMS AND A SEPARATION PRINCIPLE [J].

Benabdallah, Amel ;

Ellouze, Ines ;

Hammami, Mohamed Ali .

ASIAN JOURNAL OF CONTROL, 2011, 13 (03) :445-448

← 1 2 3 4 5 →