The existence and exponential stability of semilinear functional differential equations with random impulses under non-uniqueness

Anguraj, A.; Wu, Shujin; Vinodkumar, A.

doi:10.1016/j.na.2010.07.007

Cited by 40 publications

(25 citation statements)

References 9 publications

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“…Ravi Agarwal et al [23] proved exponential stability for differential equations with random impulses at random times. For further study, refer to [21,22,[24][25][26][27][28][29][30] and the references therein. So far there has been no paper reported dealing with uncertain random impulsive delay differential systems.…”

Section: Introductionmentioning

confidence: 99%

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

Vinodkumar

Senthilkumar

2018

Adv Differ Equ

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In this paper, we establish some criteria on robust exponential stability by using the formula for the variation of parameters and estimating the Cauchy matrix. More importantly, the robust stability criteria do not require the stability of the corresponding continuous system, and so they can be more widely applied to stabilize the unstable continuous system with time delays and uncertainties by using random impulsive control. Further, we give some numerical examples to illustrate the theoretical results.

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Section: Introductionmentioning

confidence: 99%

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

Vinodkumar

Senthilkumar

2018

Adv Differ Equ

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“…The existence and uniqueness of differential system with random impulses is studied by Anguraj et al in [11,12]. In [13], Wu and Duan discussed the oscillation, stability and boundedness of second-order differential systems with random impulses, and in [14,15], the authors proved the existence and stability results of random impulsive semilinear differential systems.…”

Section: Introductionmentioning

confidence: 99%

Existence Results for Fractional Neutral Functional Differential Equations with Random Impulses

Anguraj¹,

Ranjini

Rivero

et al. 2015

Mathematics

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“…Also, there has been a significant development in theory of impulsive differential equation. For example, [10][11][12][13][14][15][16][17] studied the existence and stability of systems. In this paper, we investigate the permanence and global attractivity of a periodic impulsive system (see (7a) and (7b)).…”

Section: Introductionmentioning

confidence: 99%

Analysis of a Periodic Single Species Population Model Involving Constant Impulsive Perturbation

Tan

Guo

et al. 2014

Journal of Applied Mathematics

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This is a continuation of the work of Tan et al. (2012). In this paper a periodic single species model controlled by constant impulsive perturbation is investigated. The constant impulse is realized at fixed moments of time. With the help of the comparison theorem of impulsive differential equations and Lyapunov functions, sufficient conditions for the permanence and global attractivity are established, respectively. Also, by comparing the above results with corresponding known results of Tan et al. (2012) (i.e., the above model with linear impulsive perturbations), we find that the two different types of impulsive perturbations have influence on the above dynamics. Numerical simulations are presented to substantiate our analytical results.

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The existence and exponential stability of semilinear functional differential equations with random impulses under non-uniqueness

Cited by 40 publications

References 9 publications

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

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

Existence Results for Fractional Neutral Functional Differential Equations with Random Impulses

Analysis of a Periodic Single Species Population Model Involving Constant Impulsive Perturbation

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