Practical exponential stability of stochastic delayed systems with G-Brownian motion via vector G-Lyapunov function

De-jun, Zhu

doi:10.1016/j.matcom.2022.04.002

Cited by 4 publications

(2 citation statements)

References 37 publications

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“…In [43], the author studied the PEISS of stochastic delayed nonlinear systems with respect to distributed external disturbances. In [44], the author studied the G-Lyapunov function on PES of stochastic delayed systems via G-Brownian motion. In [45], the author studied the PES of stochastic impulsive systems.…”

Section: Introductionmentioning

confidence: 99%

Event-triggered controller on practically exponential input-to-state stabilization of stochastic reaction-diffusion neural networks and its application to image encryption

Gokulakrishnan

Sriniva

2023

Preprint

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The stabilization problem for a class of stochastic reaction-diffusion delayed Cohen-Grossberg neural networks (SRDDCGNNs) with event-triggered controller is addressed in this paper. To address such a problem, Neumann boundary condition, distributed and boundary external disturbances are introduced. New sufficient criteria are derived by using the Lyapunov method, event-triggered mechanism, and the linear matrix inequality (LMI) approach to ensure the proposed controlled systems achieve practically exponential input-to-state stabilization. In light of these criteria, the impact of an event-triggered controller on practically exponential input-to-state stability (PEISS) is examined. Furthermore , the obtained results are successfully applied to stochastic reaction-diffusion delayed cellular neural networks (SRDDCNNs) and stochastic reaction-diffusion delayed Hopfield neural networks (SRD-DHNNs). At last, simulation results are given to illustrate the main results, and the SRDDHNNs are applied to the image encryption.

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Section: Introductionmentioning

confidence: 99%

Event-triggered controller on practically exponential input-to-state stabilization of stochastic reaction-diffusion neural networks and its application to image encryption

Gokulakrishnan

Sriniva

2023

Preprint

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“…Noise is used to destabilize a given stable system whereas it can also be used to stabilize a given unstable system or to make a given stable system even more stable. The asymptotic behaviors of solutions of some classes of stochastic systems have been studied by many authors (see [3], [18], [23], [27], [30], [31]- [33]).…”

Section: Introductionmentioning

confidence: 99%

Estimates of Exponential Convergence for Solutions of Stochastic Nonlinear Systems

2023

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This paper aims to analyze the behavior of the solutions of a stochastic perturbed system with respect to the solutions of the stochastic unperturbed system. To prove our stability results, we have derived a new Gronwall-type inequality instead of the Lyapunov techniques, which makes it easy to apply in practice and it can be considered as a more general tool in some situations. On the one hand, we present sufficient conditions ensuring the global practical uniform exponential stability of SDEs based on Gronwall's inequalities. On the other hand, we investigate the global practical uniform exponential stability with respect to a part of the variables of the stochastic perturbed system by using generalized Gronwall's inequalities. It turns out that, the proposed approach gives a better result comparing with the use of a Lyapunov function. A numerical example is presented to illustrate the applicability of our results.

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Event-Triggered Controller on Practically Exponential Input-to-State Stabilization of Stochastic Reaction–Diffusion Cohen–Grossberg Neural Networks and Its Application to Image Encryption

Gokulakrishnan

Srinivasan

2023

Neural Process Lett

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Practical exponential stability of stochastic delayed systems with G-Brownian motion via vector G-Lyapunov function

Cited by 4 publications

References 37 publications

Event-triggered controller on practically exponential input-to-state stabilization of stochastic reaction-diffusion neural networks and its application to image encryption

Event-triggered controller on practically exponential input-to-state stabilization of stochastic reaction-diffusion neural networks and its application to image encryption

Estimates of Exponential Convergence for Solutions of Stochastic Nonlinear Systems

Event-Triggered Controller on Practically Exponential Input-to-State Stabilization of Stochastic Reaction–Diffusion Cohen–Grossberg Neural Networks and Its Application to Image Encryption

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