Practical Stability of Impulsive Delay Differential Equations and Applications to Control Problems

2001 ◽  
pp. 3-21 ◽  
Author(s):  
George Ballinger ◽  
Xinzhi Liu
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Practical Stability ◽  
Control Problems ◽  
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.

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