Exponential stability of non-linear stochastic delay differential system with generalized delay-dependent impulsive points

Rengamannar, Kaviya; Balakrishnan, Ganesh Priya; Muthukumar, P.; Niezabitowski, Michał

doi:10.1016/j.amc.2020.125344

Cited by 5 publications

(10 citation statements)

References 10 publications

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“…Figure 1 displays the states for System (3). We can see that the states for System (3)can reach the equilibrium point in a finite time, which is different from the asymptotic convergence of the impulsive stochastic systems considered in the literature [5][6][7][8][9][10][11][12][13].…”

Section: Apply To a Stochastic Nonlinear Systems With Stochastic Impu...contrasting

confidence: 57%

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Stochastic Finite-Time Stability for Stochastic Nonlinear Systems with Stochastic Impulses

2022

Symmetry

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In this paper, some novel stochastic finite-time stability criteria for stochastic nonlinear systems with stochastic impulse effects are established. The results in this paper blackgeneralized the related results in from two aspects: 1. the model in is the deterministic systems, which means that the noise effect that can be described as a symmetric Markov process Brownian motion is considered in our models; 2. the stochastic finite-time stability criterion is established in this paper, not the asymptotic stability and the input-to-state stability that are studied in the form literature. Finally, an example is given to show the significance blackand usefulness of our results.

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Section: Apply To a Stochastic Nonlinear Systems With Stochastic Impu...contrasting

confidence: 57%

“…Moreover, Refs. [7,8] considered the exponential stability for impulsive stochastic delay differential systems. Ref.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Finite-Time Stability for Stochastic Nonlinear Systems with Stochastic Impulses

2022

Symmetry

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“…This 'equivalent method' has attracted the attention of many researchers, such as [4,5,[26][27][28]30,31]. Nowadays, impulsive delay differential systems have been widely studied, and a variety of applications have been found.…”

Section: Stability Of Impulsive Delay Differential Systemsmentioning

confidence: 99%

“…Some classical research methods have been successfully applied, such as the Lyapunov method, Lyapunov-Krasovskii functional, Razumikhin technique, Lie algebra, Matrix inequality, It ô's formula and so on. With the rapid development of research, scientists have proposed a variety of research methods, such as the Euler-Maruyama method, average dwell-time method [3], equivalent method [4], Runge-Kutta-Maruyama method [5], sinh-cosh method [6], sech-function method [7], variational method [8], Haar wavelet method [9] and so on. Through the application of these methods, researchers have obtained a significant number of results on stochastic systems.…”

Section: Introductionmentioning

confidence: 99%

Stability of Differential Systems with Impulsive Effects

Li,

Hui,

2023

Mathematics

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In this paper, a brief survey on the stability of differential systems with impulsive effects is provided. A large number of research results on the stability of differential systems with impulsive effects are considered. These systems include impulsive differential systems, stochastic impulsive differential systems and differential systems with several specific impulses (non-instantaneous impulses, delayed impulses, impulses suffered by logic choice and impulse time windows). The stability issues as well as the applications in neural networks are discussed in detail.

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“…For example, Refs. [39,40] considered the exponential stability for impulsive stochastic delay differential systems. Ref.…”

Section: Introductionmentioning

confidence: 99%

Stability of Impulsive Stochastic Delay Systems with Markovian Switched Delay Effects

2022

Mathematics

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In this paper, we investigate the pth moment exponential stability of impulsive stochastic delay systems with Markovian switched delay effects. The model we consider here is rather different from the models in the existing literature. In particular, the delay is a Markov chain, which is quite different from the traditional deterministic delay. By using the Markov chain theory, stochastic analysis theory, Razumikhin technology and the Lyaponov method, we derive a criterion of pth moment exponential stability for the suggested system. Finally, an example is provided to illustrate the effectiveness of the obtained result.

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Exponential stability of non-linear stochastic delay differential system with generalized delay-dependent impulsive points

Cited by 5 publications

References 10 publications

Stochastic Finite-Time Stability for Stochastic Nonlinear Systems with Stochastic Impulses

Stochastic Finite-Time Stability for Stochastic Nonlinear Systems with Stochastic Impulses

Stability of Differential Systems with Impulsive Effects

Stability of Impulsive Stochastic Delay Systems with Markovian Switched Delay Effects

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