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 Delay Differential Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Xiaotai Wu ◽  
Litan Yan ◽  
Wenbing Zhang ◽  
Liang Chen
Keyword(s):  
Exponential Stability ◽  
The Other ◽  
Stability Criteria ◽  
Differential Systems ◽  
Stochastic Delay ◽  
Almost Sure Exponential Stability ◽  
Delay Differential Systems ◽  
The Stability ◽  
Delay Differential ◽  
Average Impulsive Interval

This paper investigates the stability of stochastic delay differential systems with two kinds of impulses, that is, destabilizing impulses and stabilizing impulses. Both thepth moment and almost sure exponential stability criteria are established by using the average impulsive interval. When the impulses are regarded as disturbances, a lower bound of average impulsive interval is obtained; it means that the impulses should not happen too frequently. On the other hand, when the impulses are used to stabilize the system, an upper bound of average impulsive interval is derived; namely, enough impulses are needed to stabilize the system. The effectiveness of the proposed results is illustrated by two examples.

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 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.

Sign in / Sign up

Export Citation Format

Share Document