Stabilization in distribution of hybrid stochastic differential delay equations with Lévy noise by discrete-time state feedback controls

This paper was concerned with stabilization in distribution by feedback controls based on discrete-time state observations for a class of nonlinear stochastic differential delay equations with Markovian switching and Lévy noise (SDDEs-MS-LN). Compared with previous literature, we employed Lévy noise in the discussion about stabilization in distribution for hybrid stochastic delay systems and we considered using a discrete-time linear feedback control which is more realistic and costs less. In addition, by constructing a new Lyapunov functional, stabilization in distribution of controlled systems can be achieved with the coefficients satisfying globally Lipschitz conditions. In particular, we discussed the design of feedback controls in two structure cases: state feedback and output injection. At the same time, the lower bound for the duration between two consecutive observations $\tau$ ( ${\tau }^{\ast }$) was obtained as well. Finally, a numerical experiment with some computer simulations was given to illustrate the new results.