Exponential Stability Analysis for Stochastic Delayed Differential Systems with Impulsive Effects: Average Impulsive Interval Approach

2016 ◽  
Vol 19 (1) ◽  
pp. 74-86 ◽  
Author(s):  
Fengqi Yao ◽  
Jinde Cao ◽  
Li Qiu ◽  
Pei Cheng
Keyword(s):  
Stability Analysis ◽  
Exponential Stability ◽  
Impulsive Effects ◽  
Differential Systems ◽  
Interval Approach ◽  
Average Impulsive Interval

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 Stability Analysis of Discrete-Time Stochastic Delay Systems with Impulses

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 418
Author(s):  
Ting Cai ◽  
Pei Cheng
Keyword(s):  
Stability Analysis ◽  
Exponential Stability ◽  
Discrete Time ◽  
Delay Systems ◽  
Stochastic Delay ◽  
Average Value ◽  
Varying Coefficients ◽  
Time Varying Coefficients ◽  
Average Impulsive Interval ◽  
Moment Exponential Stability

This paper is concerned with stability analysis of discrete-time stochastic delay systems with impulses. By using the sums average value of the time-varying coefficients and the average impulsive interval, two sufficient criteria for exponential stability of discrete-time impulsive stochastic delay systems are derived, which are more convenient to be applied than those Razumikhin-type conditions in previous literature. Both pth moment asymptotic stability and pth moment exponential stability are considered. Finally, two numerical examples to illustrate the effectiveness.

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