Polynomial stabilization of hybrid PSDEs with highly nonlinear coefficient and Lévy noise

This paper investigates the realization of $H_{\infty }$ stabilization and polynomial stabilization for a class of hybrid stochastic systems with Lévy noise and pantograph delays, a specific form of unbounded delays. Unlike the conventional linear growth condition, the drift and diffusion terms in this system are only required to meet the polynomial growth condition, which is much weaker than linear growth condition. By designing discrete-time delay feedback control strategies and leveraging M-matrix theory and Lyapunov functionals, we demonstrate that the controlled system can achieve $H_{\infty }$ stabilization, polynomial stabilization, and almost sure polynomial stability. Additionally, we provide an upper bound on the time lag in the discrete-time delay feedback control. The theoretical results are further validated through a numerical simulation presented at the end of the paper.