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

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.

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

Stabilization , L\'evy noise , stochastic differential delay equations , delay feedback control