Stability analysis of highly nonlinear hybrid stochastic systems with Poisson jump

Abstract

This article discusses a class of nonlinear hybrid stochastic differential delay equations with Poisson jump and different structures. Compared with the Brownian motion, the jump makes the analysis more complex by reason of the discontinuity of its sample paths. Moreover, the coefficients meet a novel nonlinear growth condition and different structures in different switch modes. By using M-matrices and Lyapunov functions, we prove that the existence-uniqueness, asymptotic boundedness and exponential stability of the solution. Finally, we give two examples to demonstrate the usefulness of our theory.