Stabilization by delay feedback control for highly nonlinear HSDDEs driven by Lévy noise

Document Type : Research Article

Author

School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454003, China

Abstract

This research aims to investigate the stabilization of highly nonlinear hybrid stochastic differential delay equations (HSDDEs) with L'evy noise by delay feedback control. The coefficients of these systems satisfy a more general polynomial growth condition instead of classical linear growth condition. Precisely, an appropriate Lyapunov functional is constructed to analyze the stabilization of such systems in the sense of $H_{\infty}$-stability and asymptotic stability. The theoretical analysis indicates that the delay can affect the stability of highly nonlinear hybrid stochastic systems.  

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Journal of Mathematical Modeling
Volume 12, Issue 4
December 2024
Pages 769-779

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