scholarly journals Practical Stability and Integral Stability for Singular Differential Systems with Maxima

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Junyan Bao ◽  
Peiguang Wang ◽  
Yanjun Li
Keyword(s):  
Comparison Principle ◽  
Lyapunov Method ◽  
Practical Stability ◽  
Differential Systems ◽  
Integral Stability

In this paper, we introduce various definitions of practical stability and integral stability for nonlinear singular differential systems with maxima and give criteria of stability for such systems via the Lyapunov method and comparison principle.

scholarly journals Integral Stability in Terms of Two Measures for Nonlinear Differential Systems with “Maxima”

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Peiguang Wang ◽  
Qing Xu ◽  
Xiaojing Liu
Keyword(s):  
Comparison Principle ◽  
Lyapunov Functions ◽  
Differential Systems ◽  
Two Measures ◽  
Integral Stability ◽  
Nonlinear Differential Systems

This paper investigates relatively integral stability in terms of two measures for two differential systems with “maxima” by employing Lyapunov functions, Razumikhin method, and comparison principle. An example is given to illustrate our result.

scholarly journals Practical stability, boundedness criteria and Lagrange stability of fuzzy differential systems

2012 ◽  
Vol 64 (6) ◽  
pp. 2118-2127 ◽  
Author(s):  
Coşkun Yakar ◽  
Muhammed Çi̇çek ◽  
M. Bayram Gücen
Keyword(s):  
Practical Stability ◽  
Differential Systems ◽  
Lagrange Stability

scholarly journals pth Mean Practical Stability for Large-Scale Itô Stochastic Systems with Markovian Switching

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Yan Yun ◽  
Huisheng Shu ◽  
Yan Che
Keyword(s):  
Comparison Principle ◽  
Large Scale ◽  
Stochastic Systems ◽  
Markovian Switching ◽  
Practical Stability ◽  
Nonlinear Stochastic Systems ◽  
Deterministic Systems ◽  
The One

Motivated by the study of a class of large-scale stochastic systems with Markovian switching, this correspondence paper is concerned with the practical stability in thepth mean. By investigating Lyapunov-like functions and the basic comparison principle, some criteria are derived for various types of practical stability in thepth mean of nonlinear stochastic systems. The main contribution of these results is to convert the problem of practical stability in thepth mean of stochastic systems into the one of practical stability of the comparative deterministic systems.

scholarly journals Stability for Caputo Fractional Differential Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Sung Kyu Choi ◽  
Bowon Kang ◽  
Namjip Koo
Keyword(s):  
Comparison Principle ◽  
Direct Method ◽  
Stability Of Solutions ◽  
Lyapunov Direct Method ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Fractional Differential

We introduce the notion ofh-stability for fractional differential systems. Then we investigate the boundedness andh-stability of solutions of Caputo fractional differential systems by using fractional comparison principle and fractional Lyapunov direct method. Furthermore, we give examples to illustrate our results.

Lyapunov method for nonlinear fractional differential systems with delay

2015 ◽  
Vol 82 (1-2) ◽  
pp. 1015-1025 ◽  
Author(s):  
Yanhua Wen ◽  
Xian-Feng Zhou ◽  
Zhixin Zhang ◽  
Song Liu
Keyword(s):  
Lyapunov Method ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Fractional Differential

On practical stability of perturbed differential systems

2005 ◽  
Vol 163 (3) ◽  
pp. 1055-1060 ◽  
Author(s):  
A.A. Soliman
Keyword(s):  
Practical Stability ◽  
Differential Systems

scholarly journals A comparison principle and stability for large-scale impulsive delay differential systems

2005 ◽  
Vol 47 (2) ◽  
pp. 203-235 ◽  
Author(s):  
Xinzhi Liu ◽  
Xuemin Shen ◽  
Yi Zhang
Keyword(s):  
Comparison Principle ◽  
Large Scale ◽  
Sufficient Conditions ◽  
Neutral Systems ◽  
Differential Systems ◽  
Impulsive Delay ◽  
Linear And Nonlinear ◽  
Delay Differential Systems ◽  
The Stability ◽  
Delay Differential

AbstractThis paper studies the stability of large-scale impulsive delay differential systems and impulsive neutral systems. By developing some impulsive delay differential inequalities and a comparison principle, sufficient conditions are derived for the stability of both linear and nonlinear large-scale impulsive delay differential systems and impulsive neutral systems. Examples are given to illustrate the main results.

scholarly journals Impulsive Fractional Integrodifferential Equations and Lyapunov Method for Existence of Almost Periodic Solutions

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Gani Tr. Stamov
Keyword(s):  
Periodic Solutions ◽  
Comparison Principle ◽  
Lyapunov Method ◽  
Integrodifferential Equations ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Stability Behavior ◽  
The Stability

The plan of this paper is to find conditions for the existence of almost periodic solutions for a class of impulsive fractional integrodifferential equations. The investigations are carried out by using a new fractional comparison principle, coupled with the fractional Lyapunov method. The stability behavior of the almost periodic solutions is also considered, extending the corresponding theory of impulsive integrodifferential equations.

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