Stability and stabilization of switching stochastic differential equations subject to probabilistic state jumps

Stability conditions of continuous-time mode switching stochastic systems with probabilistic state jumps are provided. The mode signal, which manages the transition between subsystems, is modeled as a piecewise constant stochastic process. The state variables of the stochastic switching system is subject to jumps of random size occurring at random instances. The proposed piecewise continuous control law guarantees exponential moment stability of the zero solution by using multiple Lyapunov functions. Finally, an illustrative numerical example is presented to demonstrate the efficacy of our results.