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 Second-Order Impulsive Delay Differential Systems: Necessary and Sufficient Conditions for Oscillatory or Asymptotic Behavior

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 722
Author(s):  
Shyam Sundar Santra ◽  
Khaled Mohamed Khedher ◽  
Osama Moaaz ◽  
Ali Muhib ◽  
Shao-Wen Yao
Keyword(s):  
Asymptotic Behavior ◽  
Differential System ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
Sufficient And Necessary Conditions ◽  
Impulsive Delay ◽  
Delay Differential Systems ◽  
Delay Differential ◽  
Necessary And Sufficient

In this work, we aimed to obtain sufficient and necessary conditions for the oscillatory or asymptotic behavior of an impulsive differential system. It is easy to notice that most works that study the oscillation are concerned only with sufficient conditions and without impulses, so our results extend and complement previous results in the literature. Further, we provide two examples to illustrate the main results.

scholarly journals Stability of linear neutral delay-differential systems

1988 ◽  
Vol 38 (3) ◽  
pp. 339-344 ◽  
Author(s):  
Li-Ming Li
Keyword(s):  
Differential Inequality ◽  
Sufficient Conditions ◽  
Neutral Delay ◽  
Differential Systems ◽  
Delay Differential Systems ◽  
The Stability ◽  
Delay Differential ◽  
Delay Differential Inequality

Sufficient conditions are obtained for the stability of linear neutral delay-differential systems by using a delay-differential inequality.

scholarly journals Stability Analysis for Fractional-Order Linear Singular Delay Differential Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Hai Zhang ◽  
Daiyong Wu ◽  
Jinde Cao ◽  
Hui Zhang
Keyword(s):  
Asymptotic Stability ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Algebraic Approach ◽  
Differential Systems ◽  
Order Linear ◽  
Delay Differential Systems ◽  
The Stability ◽  
Delay Differential ◽  
Theoretical Results

We investigate the delay-independently asymptotic stability of fractional-order linear singular delay differential systems. Based on the algebraic approach, the sufficient conditions are presented to ensure the asymptotic stability for any delay parameter. By applying the stability criteria, one can avoid solving the roots of transcendental equations. An example is also provided to illustrate the effectiveness and applicability of the theoretical results.

Finite time stability of semilinear multi-delay differential systems

2017 ◽  
Vol 40 (9) ◽  
pp. 2948-2959
Author(s):  
JinRong Wang ◽  
Zijian Luo
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Time Stability ◽  
Differential Systems ◽  
Finite Time Stability ◽  
Alternative Approach ◽  
Representation Of Solutions ◽  
Delay Differential Systems ◽  
Delay Differential ◽  
Exponential Matrix

In this paper, we provide an alternative approach to study finite time stability for semilinear multi-delay differential systems with pairwise permutable matrices associated with the stand and generalized Landau symbol conditions for nonlinear terms. The explicit representation of solutions involving a special multi-delayed exponential matrix function is developed to establish sufficient conditions to guarantee the systems are finite time stable by virtue of Gronwall integral inequalities with delay. Finally, we demonstrate the validity of the designed method and discuss it using numerical examples.

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