H∞ and Asymptotic Stability via delay feedback for hybrid neutral stochastic delay differential equations with Lévy noise

Abstract

This work addresses existence and stabilization problem for a hybrid neutral stochastic delay differential equations with Lévy noise (HNSDDELN). The coefficients of such systems do not satisfy the conventional linear growth conditions, but are subject to high nonlinearity. We first prove the existence and uniqueness of the solution. We then design a delay feedback controller to make an unstable HNSDDELN $H_{\infty }$ and asymptotically stable in ${\mathbb{L}}^{p}$ . We end up with a numerical example that corroborates our theoretical findings.