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

• Published in: IEEE transactions on automatic control Vol. 70; no. 2; pp. 1176 - 1183
• Main Author: Zhu, Quanxin
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.02.2025; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Control theory; Delays; Discrete time systems; Event-triggered feedback control; event-triggered sampling; Linear matrix inequalities; Lipschitz condition; Neural networks; Nonlinear systems; practically <named-content xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" content-type="math" xlink:type="simple"> <inline-formula> <tex-math notation="LaTeX"> p</tex-math> </inline-formula> </named-content>th moment exponential stability; Process control; Sampling; Stability; Stabilization; stochastic neural network; stochastic nonlinear delay systems (SNDSs) driven by Lévy processes; Stochastic processes; Stochastic systems
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2024.3448128

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><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><tex-math notation="LaTeX">p</tex-math></inline-formula>th moment exponential stabilization criterion for any <inline-formula><tex-math notation="LaTeX">p>0</tex-math></inline-formula>, which is more general and meaningful for practical application than those results only considering the case of <inline-formula><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.