Exponential Synchronization of Infinite-Dimensional Stochastic Systems With Poisson Jumps Under Aperiodically Intermittent Impulse Control

Lili Chen; Yiqun Liu; Yanfeng Zhao; Zhen Wang

IEEE/CAA Journal of Automatica Sinica

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L. Chen, Y. Liu, Y. Zhao, and Z. Wang, “Exponential synchronization of infinite-dimensional stochastic systems with poisson jumps under aperiodically intermittent impulse control,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 2, pp. 1–11, Feb. 2026.

Citation:

L. Chen, Y. Liu, Y. Zhao, and Z. Wang, “Exponential synchronization of infinite-dimensional stochastic systems with poisson jumps under aperiodically intermittent impulse control,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 2, pp. 1–11, Feb. 2026.

Citation:

L. Chen, Y. Liu, Y. Zhao, and Z. Wang, “Exponential synchronization of infinite-dimensional stochastic systems with poisson jumps under aperiodically intermittent impulse control,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 2, pp. 1–11, Feb. 2026.

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Exponential Synchronization of Infinite-Dimensional Stochastic Systems With Poisson Jumps Under Aperiodically Intermittent Impulse Control

Funds: This work was supported in part by the National Natural Science Foundation of China (12471422, 62173214, 12371173), the Natural Science Foundation of Shandong Province of China (ZR2022LLZ003, ZR2024MF001), and the Funding for Visiting Studies and Research by Teachers in Ordinary Undergraduate Colleges and Universities in Shandong Province

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Author Bio:
Lili Chen received the B.S. and M.S. degrees from Harbin University of Science and Technology, in 0000, and the Ph.D. degree from Harbin Institute of Technology, in 0000. She is currently an Academic Professor with the College of Mathematics and Systems Science, Shandong University of Science and Technology. She is a Commentator of the American Mathematical Review, a Member of the Chinese Mathematical Society, and a Member of the American Mathematical Society. Her research interests include stability and synchronization of complex Networks, distributed optimization algorithms for multi agent systems, fixed point theory and their applications

Yiqun Liu received the B.S. degree in statistics from Shandong University of Science and Technology in 2021. He is currently a master student with the College of Mathematics and Systems Science, Shandong University of Science and Technology. His current research interests include synchronization theory and Infinite-dimensional Dynamical Systems Theory

Yanfeng Zhao received the B.S. degree in information and computation science and the M.S. degree in basic mathematics from Harbin University of Science and Technology, in 2004 and 2009, respectively, and the Ph.D. degree in control theory and control engineering from the Harbin Engineering University. He is currently an Associate Professor with the College of Mathematics and System Science, Shandong University of Science and Technology. His current research interests include complex dynamical systems, neural networks, event-triggered control and attack detection

Zhen Wang (Member, IEEE) received the B.S. degree in mathematics from the Ocean University of China, in 2004, and the Ph.D. degree in control theory and control engineering from the School of Automation, Nanjing University of Science and Technology, in 2014. He has been with Shandong University of Science and Technology, since 2004, where he is currently a Professor and a Doctoral Supervisor. His current research interests include nonlinear control, neural networks, and network-based systems control
Corresponding author: Lili Chen, e-mail: cll2119@sdust.edu.cn; Yanfeng Zhao, e-mail: zhaoyf1101@sdust.edu.cn
Received Date: 2024-12-10
Revised Date: 2025-01-24
Accepted Date: 2025-02-25

Available Online: 2026-01-28

Abstract

Abstract

A novel aperiodically intermittent impulse control (AIIC) method is proposed to investigate the exponential synchronization in mean square (ESMS) of a class of impulsive stochastic infinite-dimensional systems with Poisson jumps (ISIDSP). The AIIC control strategy inherits the flexibility of aperiodically intermittent control, inclduing the variable control period, adjustable control interval length, and the discretization of impulsive control. In addition, this article introduces a novel mild Itô’s formula. By leveraging semigroup theory, the contraction mapping principle, and graph theory, along with constructing the Lyapunov function, the criterion for the existence and uniqueness of a mild solution of ISIDSP is thereby established. Furthermore, the mean-square exponential synchronization problem of the above systems is resolved, and the constraints within the mild solution domain is alleviated. These criteria clarify the impact of control parameters, control intervals and network topology on ESMS. The theoretical results are subsequently applied to a class of neural networks with reaction-diffusion processes, and the validity of the results is verified using numerical simulations.
- Complex network,
- exponential synchronization,
- impulse control,
- infinite dimensional system,
- intermittent control

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Exponential Synchronization of Infinite-Dimensional Stochastic Systems With Poisson Jumps Under Aperiodically Intermittent Impulse Control

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