Almost sure exponential stabilization and suppression by periodically intermittent stochastic perturbation with jumps

The main aim of this article is to examine almost sure exponential stabilization and suppression of nonlinear systems by periodically intermittent stochastic perturbation with jumps. On the one hand, some sufficient criteria ensure almost sure stabilization of the unstable deterministic system by applying exponential martingale inequality with jumps. On the other hand, sufficient conditions of destabilization are provided under which the system is stable by the well-known strong law of large numbers of local martingale and Poisson process. Both the sample Lyapunov exponents are closely related to the control period \begin{document}$ T $\end{document} and noise width \begin{document}$ \theta $\end{document} . As for applications, the well-known Lorenz chaotic systems and nonlinear Lienard equation with jumps are discussed. Finally, two simulation examples demonstrating the effectiveness of the results are provided.