Global exponential stability of impulsive stochastic functional differential systems

2010 ◽  
Vol 80 (23-24) ◽  
pp. 1854-1862 ◽  
Author(s):  
Pei Cheng ◽  
Feiqi Deng
Keyword(s):  
Exponential Stability ◽  
Global Exponential Stability ◽  
Differential Systems ◽  
Functional Differential Systems ◽  
Functional Differential ◽  
Stochastic Functional

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 Impulsive Stability of Stochastic Functional Differential Systems Driven by G-Brownian Motion

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 227
Author(s):  
Lijun Pan ◽  
Jinde Cao ◽  
Yong Ren
Keyword(s):  
Brownian Motion ◽  
Exponential Stability ◽  
Differential Systems ◽  
Stability Theorems ◽  
Functional Differential Systems ◽  
Functional Differential ◽  
The Stability ◽  
Delay Dependent ◽  
Moment Exponential Stability ◽  
Stochastic Functional

This paper is concerned with the p-th moment exponential stability and quasi sure exponential stability of impulsive stochastic functional differential systems driven by G-Brownian motion (IGSFDSs). By using G-Lyapunov method, several stability theorems of IGSFDSs are obtained. These new results are employed to impulsive stochastic delayed differential systems driven by G-motion (IGSDDEs). In addition, delay-dependent method is developed to investigate the stability of IGSDDSs by constructing the G-Lyapunov–Krasovkii functional. Finally, an example is given to demonstrate the effectiveness of the obtained results.

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.

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