Estimates of exponential convergence for solutions of stochastic nonlinear systems
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 appl...
| Autores: | , , |
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| Formato: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2023 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/150157 |
| Acesso em linha: | https://hdl.handle.net/11441/150157 https://doi.org/10.1007/s00245-023-10040-2 |
| Access Level: | acceso abierto |
| Palavra-chave: | Stochastic differential equations Gronwall’s inequalities Practical uniform exponential stability Practical uniform exponential stability with respect to a part of the variables |
| Resumo: | 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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