scholarly journals New Results on Global Exponential Stability of Impulsive Functional Differential Systems with Delayed Impulses

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Pei Cheng ◽  
Zheng Wu ◽  
Lianglong Wang
Keyword(s):  
Exponential Stability ◽  
Lyapunov Functions ◽  
Global Exponential Stability ◽  
Differential Systems ◽  
Continuous Flows ◽  
Functional Differential Systems ◽  
Functional Differential ◽  
Delayed Impulses

By using the Lyapunov functions and the Razumikhin techniques, the exponential stability of impulsive functional differential systems with delayed impulses is investigated. The obtained results have shown that the system will stable if the impulses’ frequency and amplitude are suitably related to the increase or decrease of the continuous flows, and they improve and complement ones from some recent works. An example is provided to illustrate the effectiveness and the advantages of the results obtained.

scholarly journals Exponential Stability of Impulsive Stochastic Functional Differential Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Zheng Wu ◽  
Hao Huang ◽  
Lianglong Wang
Keyword(s):  
Exponential Stability ◽  
Lyapunov Functions ◽  
Differential Systems ◽  
Stochastic Delay ◽  
Almost Sure Exponential Stability ◽  
Functional Differential Systems ◽  
Functional Differential ◽  
Delay Differential Systems ◽  
Delay Differential ◽  
Stochastic Functional

This paper is concerned with stabilization of impulsive stochastic delay differential systems. Based on the Razumikhin techniques and Lyapunov functions, several criteria onpth moment and almost sure exponential stability are established. Our results show that stochastic functional differential systems may be exponentially stabilized by impulses.

scholarly journals Exponential Stability of Impulsive Stochastic Functional Differential Systems with Delayed Impulses

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Fengqi Yao ◽  
Feiqi Deng ◽  
Pei Cheng
Keyword(s):  
Exponential Stability ◽  
Delay Systems ◽  
Differential Systems ◽  
Stochastic Delay ◽  
Functional Differential Systems ◽  
Two Measures ◽  
Functional Differential ◽  
The Stability ◽  
Delayed Impulses ◽  
Stochastic Functional

A class of generalized impulsive stochastic functional differential systems with delayed impulses is considered. By employing piecewise continuous Lyapunov functions and the Razumikhin techniques, several criteria on the exponential stability and uniform stability in terms of two measures for the mentioned systems are obtained, which show that unstable stochastic functional differential systems may be stabilized by appropriate delayed impulses. Based on the stability results, delayed impulsive controllers which mean square exponentially stabilize linear stochastic delay systems are proposed. Finally, numerical examples are given to verify the effectiveness and advantages of our results.

scholarly journals Impulsive Exponential Stabilization of Functional Differential Systems with Infinite Delay

2009 ◽  
Vol 2009 ◽  
pp. 1-12
Author(s):  
Xiaoli Sun ◽  
Xiaodi Li
Keyword(s):  
Lyapunov Functions ◽  
Infinite Delay ◽  
Exponential Stabilization ◽  
Differential Systems ◽  
Unstable Systems ◽  
Razumikhin Technique ◽  
Numerical Example ◽  
Functional Differential Systems ◽  
Functional Differential

By using the Razumikhin technique and Lyapunov functions, we investigated the impulsive exponential stabilization of functional differential systems with infinite delay. A new result on the exponential stabilization by impulses is gained. Our result shows that impulses can make unstable systems stable. A numerical example is given to illustrate the feasibility of the result.

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