scholarly journals Stability criteria for impulsive differential equations in terms of two measures

1989 ◽  
Vol 137 (2) ◽  
pp. 591-604 ◽  
Author(s):  
V Lakshmikantham ◽  
Xinzhi Liu
Keyword(s):  
Differential Equations ◽  
Impulsive Differential Equations ◽  
Stability Criteria ◽  
Two Measures

scholarly journals On the Practical Stability of Impulsive Differential Equations with Infinite Delay in Terms of Two Measures

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Bo Wu ◽  
Jing Han ◽  
Xiushan Cai
Keyword(s):  
Differential Equations ◽  
Lyapunov Functions ◽  
Infinite Delay ◽  
Impulsive Differential Equations ◽  
Practical Stability ◽  
Stability Criteria ◽  
Razumikhin Technique ◽  
Two Measures

We consider the practical stability of impulsive differential equations with infinite delay in terms of two measures. New stability criteria are established by employing Lyapunov functions and Razumikhin technique. Moreover, an example is given to illustrate the advantage of the obtained result.

scholarly journals The Mean Stability Criteria in terms of Two Measures for Stochastic Differential Equations with Coefficient’s Uncertainty

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Rui Zhang ◽  
Yinjing Guo ◽  
Xiangrong Wang ◽  
Xueqing Zhang
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Stochastic Stability ◽  
Stochastic Systems ◽  
Stability Criteria ◽  
Two Measures ◽  
The Mean ◽  
The Stability

This paper extends the stochastic stability criteria of two measures to the mean stability and proves the stability criteria for a kind of stochastic Itô’s systems. Moreover, by applying optimal control approaches, the mean stability criteria in terms of two measures are also obtained for the stochastic systems with coefficient’s uncertainty.

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