scholarly journals Exponential stability of the exact solutions and the numerical solutions for a class of linear impulsive delay differential equations

2015 ◽  
Vol 285 ◽  
pp. 32-44 ◽  
Author(s):  
G.L. Zhang ◽  
M.H. Song ◽  
M.Z. Liu
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Exact Solutions ◽  
Delay Differential Equations ◽  
Numerical Solutions ◽  
Impulsive Delay Differential Equations ◽  
Impulsive Delay ◽  
Delay Differential

scholarly journals Exponential Stability of Impulsive Delay Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
G. L. Zhang ◽  
M. H. Song ◽  
M. Z. Liu
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Euler Method ◽  
Exponentially Stable ◽  
Impulsive Delay Differential Equations ◽  
Numerical Process ◽  
Impulsive Delay ◽  
Delay Differential

The main objective of this paper is to further investigate the exponential stability of a class of impulsive delay differential equations. Several new criteria for the exponential stability are analytically established based on Razumikhin techniques. Some sufficient conditions, under which a class of linear impulsive delay differential equations are exponentially stable, are also given. An Euler method is applied to this kind of equations and it is shown that the exponential stability is preserved by the numerical process.

Exponential Stability of Impulsive Delay Differential Equations by using Weight Function

2018 ◽  
Vol 7 (3) ◽  
pp. 247-251
Author(s):  
Palwinder Singh ◽  
Sanjay K. Srivastava ◽  
Kanwalpreet Kaur
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Weight Function ◽  
Delay Differential Equations ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Impulsive Delay Differential Equations ◽  
Impulsive Delay ◽  
Delay Differential

Abstract In present study, some sufficient conditions for the exponential stability of impulsive delay differential equations are obtained by introducing weight function in the norm and applying the concept of Lyapunov functions and Razumikhin techniques. The function ψ plays the role of weight and hence increases the rate of convergence towards stability. The obtained results are demonstrated with examples.

scholarly journals Stability Analysis of Analytical and Numerical Solutions to Nonlinear Delay Differential Equations with Variable Impulses

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
X. Liu ◽  
Y. M. Zeng
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Numerical Scheme ◽  
Numerical Solutions ◽  
Analytical And Numerical Solutions ◽  
Impulsive Delay Differential Equations ◽  
Nonlinear Delay Differential Equations ◽  
Impulsive Delay ◽  
Delay Differential ◽  
Nonlinear Delay

A stability theory of nonlinear impulsive delay differential equations (IDDEs) is established. Existing algorithm may not converge when the impulses are variable. A convergent numerical scheme is established for nonlinear delay differential equations with variable impulses. Some stability conditions of analytical and numerical solutions to IDDEs are given by the properties of delay differential equations without impulsive perturbations.

scholarly journals Global Exponential Stability of Impulsive Functional Differential Equations via Razumikhin Technique

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
Shiguo Peng ◽  
Liping Yang
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Delay Differential Equations ◽  
Global Exponential Stability ◽  
Functional Differential Equations ◽  
Razumikhin Technique ◽  
Impulsive Delay Differential Equations ◽  
Impulsive Delay ◽  
Functional Differential ◽  
Delay Differential

This paper develops some new Razumikhin-type theorems on global exponential stability of impulsive functional differential equations. Some applications are given to impulsive delay differential equations. Compared with some existing works, a distinctive feature of this paper is to address exponential stability problems for any finite delay. It is shown that the functional differential equations can be globally exponentially stabilized by impulses even if it may be unstable itself. Two examples verify the effectiveness of the proposed results.

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