Stabilization of Highly Nonlinear Stochastic Coupled Systems via Periodically Intermittent Control

• 成果类型: Article
• 署名作者: Liu, Yan; Liu, Jun; Li, Wenxue
• 署名单位: Harbin Institute of Technology; University of Waterloo
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3036035
• 发表日期: 2021
• 页码: 4799-4806
• 关键词: Stability criteria; oscillators; Stochastic processes; Couplings; Nonlinear systems; Lyapunov methods; Halanay-type inequality; highly nonlinear stochastic coupled systems (HNSCSs); periodically intermittent control (PIC); modified van der Pol-Duffing oscillators

摘要

This article considers the stabilization of highly nonlinear stochastic coupled systems (HNSCSs) with time delay via periodically intermittent control. This article is motivated by that known differential inequalities to deal with periodically intermittent control do not work for HNSCSs, since the coefficients of the system do not satisfy the linear growth condition. In order to cope with this problem, a novel Halanay-type inequality is established to handle periodically intermittent control, which generalizes previous results. Then, based on this differential inequality, the graph theory, and the Lyapunov method, two main theorems are shown, whose conditions indicate how the control duration, the control gain, and the coupling strength affect the realization of the stability. Then, the theoretical results are applied to the modified van der Pol-Duffing oscillators. Finally, corresponding simulation results are presented to illustrate the effectiveness of the theoretical results.