Stabilization of Highly Nonlinear Hybrid Stochastic Differential Delay Equations with Lévy Noise by Delay Feedback Control

.This paper focuses on a class of highly nonlinear stochastic differential delay equations (SDDEs) driven by Lévy noise and Markovian chain, where the drift and diffusion coefficients satisfy more general polynomial growth condition (than the classical linear growth condition). Under the local Lipschitz condition, the existence-and-unique theorem of the solution to the highly nonlinear SDDE is established. The key aim is to investigate the stabilization problem by delay feedback controls. The key features include that the time delay in the given system is time-varying and may not be differentiable, while the time lag in the feedback control can also be time-varying as long as it has a sufficiently small upper bound.Keywordshighly nonlinearitystochastic differential delay equationMarkov chainLévy noiseexponential stabilityMSC codes60J6060J2793D15