Event-Triggered Sampling Problem for Exponential Stability of Stochastic Nonlinear Delay Systems Driven by Lévy Processes

This article mainly discusses the stabilization issue for a class of stochastic nonlinear delay systems driven by Lévy processes. Based on a novel event-triggered strategy and stochastic analysis techniques, we solve the practically <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$p$</tex-math></inline-formula>th moment exponential stability problem of the considered system. Comparing with those previous results, we do not require the global Lipschitz condition and do not use the linear matrix inequality method. Also, different from many results for stochastic systems in discrete-time or stochastic systems in continuous-time driven by the usual Brownian motion, our results are mainly concentrated on the event-triggered sampling problem of stochastic systems in continuous-time driven by Lévy processes, and delays are also involved. Moreover, we establish the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$p$</tex-math></inline-formula>th moment exponential stabilization criterion for any <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$p&gt;0$</tex-math></inline-formula>, which is more general and meaningful for practical application than those results only considering the case of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$p =2$</tex-math></inline-formula>. Finally, our results are applied to stochastic neural networks driven by Lévy processes and are checked with two examples.