Stabilisation in distribution by delay feedback control for stochastic differential equations with Markovian switching and Lévy noise

This paper is devoted to the stability in distribution of stochastic differential equations with Markovian switching and Lévy noise by delay feedback control. By constructing efficient Lyapunov functional and linear delay feedback controls, the stability in distribution of stochastic differential equations with Markovian switching and Lévy noise is accomplished with the coefficients satisfying globally Lipschitz continuous. Moreover, the design methods of feedback control under two structures of state feedback and output injection are discussed. Finally, a numerical experiment and new algorithm are provided to sustain the new results.