scholarly journals Robust exponential stability results for uncertain infinite delay differential systems with random impulsive moments

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
A Vinodkumar ◽  
T Senthilkumar ◽  
Xiaodi Li
Keyword(s):  
Exponential Stability ◽  
Infinite Delay ◽  
Robust Exponential Stability ◽  
Differential Systems ◽  
Delay Differential Systems ◽  
Delay Differential ◽  
Stability Results

scholarly journals Exponential Stability Results on Random and Fixed Time Impulsive Differential Systems with Infinite Delay

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 843
Author(s):  
Xiaodi Li ◽  
A. Vinodkumar ◽  
T. Senthilkumar
Keyword(s):  
Exponential Stability ◽  
Infinite Delay ◽  
Fixed Time ◽  
Random Time ◽  
Differential Systems ◽  
Razumikhin Technique ◽  
Comparative Results ◽  
The Stability ◽  
Delay Differential ◽  
Stability Results

In this paper, we investigated the stability criteria like an exponential and weakly exponential stable for random impulsive infinite delay differential systems (RIIDDS). Furthermore, we proved some extended exponential and weakly exponential stability results for RIIDDS by using the Lyapunov function and Razumikhin technique. Unlike other studies, we show that the stability behavior of the random time impulses is faster than the fixed time impulses. Finally, two examples were studied for comparative results of fixed and random time impulses it shows by simulation.

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.

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