Stability of a semi-linear stochastic differential system with switching and impulse

This paper formulates and studies a kind of semi-linear stochastic differential systems with switching and impulse. By using switching Lyapunov function approach, Ito formula, impulsive differential inequality method and linear matrix equality techniques, we obtain pth moment globally asymptotically stability, pth moment globally exponentially stability and mean square stability criteria for such system. Numerical examples show the validity of the obtained results.