L2-stability of vector equations with nonlinear causal mappings

被引：0

作者：

Gil, M. I. ^{[1
]}

机构：

[1] Ben Gurion Univ Negev, Dept Math, IL-84105 Beer Sheva, Israel

来源：

DYNAMIC SYSTEMS AND APPLICATIONS | 2008年 / 17卷 / 01期

关键词：

causal mappings; differential equations; differential delay equations; difference equations with continuous time; L-2-stability; absolute stability; input-to-state stability;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Nonlinear vector equations with causal mappings are considered. These equations include differential, difference, differential-delay, integro-differential and other traditional equations. Estimates for the L-2-norm of solutions are established. The obtained estimates give us explicit conditions for the L-2-stability, absolute stability and input-to-state stability of the considered equations as well as bounds for the regions of attraction of stationary states. The suggested approach enables us to consider various classes of equations from the unified point of view.

引用

页码：201 / 219

页数：19

共 50 条

[41] Output Control Approach "Consecutive Compensator" Providing Exponential and L∞-stability for Nonlinear Systems with Delay and Disturbance [J].

Pyrkin, Anton A. ;

Bobtsov, Alexey A. ;

Kolyubin, Sergey A. ;

Faronov, Maxim V. ;

Shavetov, Sergey V. ;

Kapitanyuk, Yuriy A. ;

Kapitonov, Alexander A. .

2011 IEEE INTERNATIONAL CONFERENCE ON CONTROL APPLICATIONS (CCA), 2011, :1499-1504

[42] Existence and Stability Results of Nonlinear Random Impulsive Integro-Differential Evolution Equations with Time-Varying Delays [J].

Maqbol, Sahar M. A. ;

Jain, Rupali S. ;

Reddy, B. Surendranath .

CONTEMPORARY MATHEMATICS, 2024, 5 (01) :402-420

[43] EXISTENCE AND ULAM STABILITY OF SOLUTIONS FOR NONLINEAR CAPUTO-HADAMARD FRACTIONAL DIFFERENTIAL EQUATIONS INVOLVING TWO FRACTIONAL ORDERS [J].

Saadi, Abdelkader ;

Houas, Mohamed .

FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS, 2022, 37 (01) :89-102

[44] 2D backward stochastic Navier-Stokes equations with nonlinear forcing [J].

Qiu, Jinniao ;

Tang, Shanjian ;

You, Yuncheng .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2012, 122 (01) :334-356

[45] Formulas relating K L stability estimates of discrete-time and sampled-data nonlinear systems [J].

Nesic, D ;

Teel, AR ;

Sontag, ED .

SYSTEMS & CONTROL LETTERS, 1999, 38 (01) :49-60

[46] Stability of Solutions to Systems of Nonlinear Differential Equations with Discontinuous Right-Hand Sides: Applications to Hopfield Artificial Neural Networks [J].

Boykov, Ilya ;

Roudnev, Vladimir ;

Boykova, Alla .

MATHEMATICS, 2022, 10 (09)

[47] Existence, Uniqueness and HU-Stability Results for Nonlinear Fuzzy Fractional Volterra-Fredholm Integro-Differential Equations [J].

Hamoud, Ahmed A. ;

Mohammed, Nedal M. ;

Emadifar, Homan ;

Parvaneh, Foroud ;

Hamasalh, Faraidum K. ;

Sahoo, Soubhagya Kumar ;

Khademi, Masoumeh .

INTERNATIONAL JOURNAL OF FUZZY LOGIC AND INTELLIGENT SYSTEMS, 2022, 22 (04) :391-400

[48] Ulam Type Stability Results of Nonlinear Impulsive Volterra-Fredholm Integro-Dynamic Adjoint Equations on Time Scale [J].

Shah, Syed Omar ;

Tikare, Sanket ;

Osman, Mawia .

MATHEMATICS, 2023, 11 (21)

[49] Runge-Kutta convolution quadrature methods with convergence and stability analysis for nonlinear singular fractional integro-differential equations [J].

Zhang, Gengen ;

Zhu, Rui .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2020, 84 (84)

[50] Nonlinear Stability and Convergence of Two-Step Runge-Kutta Methods for Volterra Delay Integro-Differential Equations [J].

Yuan, Haiyan ;

Song, Cheng .

ABSTRACT AND APPLIED ANALYSIS, 2013,

← 1 2 3 4 5 →