Stability analysis of highly nonlinear hybrid stochastic systems with Poisson jump

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.(c) 2022 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Automated summary

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