基于事件触发脉冲控制的变时滞系统稳定性研究
Stability Analysis of Time-Varying Delay Systems Based on Event-Triggered Impulsive Control
摘要: 本文研究了事件触发脉冲控制下变时滞系统的稳定性问题。首先我们设计了一种由系统状态决定脉冲作用时刻的事件触发脉冲控制，证明了系统不存在Zeno现象。其次我们得到了变时滞系统在提出的事件触发脉冲控制下指数稳定的充分条件。最后仿真实验结果验证了理论方案的有效性。
Abstract: This paper investigates the stability of time-varying delay systems via an event-triggered impulsive control. Firstly, the event-triggered impulsive control is designed where the impulsive instants are determined by the system states, and Zeno-behavior is ruled out. In addition, sufficient conditions of exponential stability of time-varying delay systems are gained under the proposed event-triggered impulsive control. A numerical example is finally given to illustrate the effectiveness of the theoretical results.
文章引用：郑焕南, 孙文. 基于事件触发脉冲控制的变时滞系统稳定性研究[J]. 动力系统与控制, 2021, 10(1): 13-23. https://doi.org/10.12677/DSC.2021.101002

参考文献

[1] Mackey, M.C. and Glass, L. (1977) Oscillation and Chaos in Physiological Control Systems. Science, 197, 287-289.
[Google Scholar] [CrossRef] [PubMed]
[2] Wang, X.F., Zhong, G.Q., Tang, K.S., Man, K.F. and Liu, Z.F. (2001) Generating Chaos in Chua’s Circuit via Time-Delay Feedback. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 48, 1151-1156.
[Google Scholar] [CrossRef] 
[3] 王秀娟, 彭名书. 一类时滞交通流模型的多稳定性研究[J]. 动力系统与控制, 2019, 8(4): 278-284.
[4] Lu, J.H. and Chen, G.R. (2005) A Time-Varying Dynamical Network Model and Its Controlled Synchronization Criteria. IEEE Transactions on Automatic Control, 50, 841-846.
[Google Scholar] [CrossRef] 
[5] Zheng, C. and Cao, J.D. (2014) Robust Synchronization of Coupled Neural Networks with Mixed Delays and Uncertain Parameters by Intermittent Pinning Control. Neurocomputing, 141, 153-159.
[Google Scholar] [CrossRef] 
[6] Zhou, Q., Wu, C.W. and Shi, P. (2016) Observer-Based Adaptive Fuzzy Tracking Control of Nonlinear Systems with Time Delay and Input Saturation. Fuzzy Sets and Systems, 316, 49-68.
[Google Scholar] [CrossRef] 
[7] Li, N., Wu, X.Q. and Yang, Q.R. (2020) Fixed-Time Synchronization of Complex Dynamical Network with Impulsive Effects. IEEE Access, 8, 33072-33079.
[Google Scholar] [CrossRef] 
[8] 李嘉敏, 宾红华, 黄振坤. 具有不匹配参数的脉冲离散网络准同步[J]. 动力系统与控制, 2017, 6(4): 158-163.
[9] Li, C.D., Chen, G.R., Liao, X.F. and Fan, Z.P. (2006) Chaos Quasisynchronization Induced by Impulses with Parameter Mismatches. Chaos: An Interdisciplinary Journal of Nonlinear Science, 16, Article ID: 023102.
[Google Scholar] [CrossRef] [PubMed]
[10] Yang, Z.C. and Xu, D.Y. (2007) Stability Analysis and Design of Impulsive Control Systems with Time Delay. IEEE Transactions on Automatic Control, 52, 1448-1454.
[Google Scholar] [CrossRef] 
[11] Tang, Z., Park, J.H. and Feng, J.W. (2018) Impulsive Effects on Quasi-Synchronization of Neural Networks with Parameter Mismatches and Time-Varying Delay. IEEE Transactions on Neural Networks and Learning Systems, 29, 908-919.
[Google Scholar] [CrossRef] 
[12] Guan, Z.H., Liu, Z.W., Feng, G. and Wang, Y.W. (2010) Synchronization of Complex Dynamical Networks with Time-Varying Delays via Impulsive Distributed Control. IEEE Transactions on Circuits and Systems I: Regular Papers, 57, 2182-2195.
[Google Scholar] [CrossRef] 
[13] Sun, W., Lu, J.H., Chen, S.H. and Yu, X.H. (2014) Pinning Impulsive Control Algorithms for Complex Network. Chaos: An Interdisciplinary Journal of Nonlinear Science, 24, Article ID: 013141.
[Google Scholar] [CrossRef] [PubMed]
[14] Sun, W., Guan, J.X., Lu, J.H., Zheng, Z.G., Yu, X.H. and Chen, S.H. (2020) Synchronization of the Networked System with Continuous and Impulsive Hybrid Communications. IEEE Transactions on Neural Networks and Learning Systems, 31, 960-971.
[Google Scholar] [CrossRef] 
[15] Liu, K.X., Duan, P.H., Duan, Z.S., Cai, H.B. and Lu, J.H. (2018) Leader-Following Consensus of Multi-Agent Systems with Switching Networks and Event-Triggered Control. IEEE Transactions on Circuits and Systems I: Regular Papers, 65, 1696-1706.
[Google Scholar] [CrossRef] 
[16] Dimarogonas, D.V., Frazzoli, E. and Johansson, K.H. (2012) Distributed Event-Triggered Control for Multi-Agent Systems. IEEE Transactions on Automatic Control, 57, 1291-1297.
[Google Scholar] [CrossRef] 
[17] Lu, W.L., Han, Y.J. and Chen, T.P. (2015) Synchronization in Networks of Linearly Coupled Dynamical Systems via Event-Triggered Diffusion. IEEE Transactions on Neural Networks and Learning Systems, 26, 3060-3069.
[Google Scholar] [CrossRef] 
[18] Zhu, W., Wang, D.D., Liu, L. and Feng, G. (2018) Event-Based Impulsive Control of Continuous-Time Dynamic Systems and Its Application to Synchronization of Memristive Neural Networks. IEEE Transactions on Neural Networks and Learning Systems, 29, 3599-3609.
[Google Scholar] [CrossRef] 
[19] Sun, W., Zheng, H.N., Guo, W.L., Xu, Y.H., Cao, J.D., Mahmoud, A. and Chen, S.H. (2020) Quasi-Synchronization of Heterogeneous Dynamical Networks via Event-Triggered Impulsive Controls. IEEE Transactions on Cybernetics, 1-12.
[Google Scholar] [CrossRef] 
[20] Zhou, Y.F. and Zeng, Z.G. (2018) Event-Triggered Impulsive Control on Quasi-Synchronization of Memristive Neural Networks with Time-Varying Delays. Neural Networks, 110, 55-65.
[Google Scholar] [CrossRef] [PubMed]
[21] 曹娟. 自适应间歇控制下时滞复杂网络的有限时同步[J]. 动力系统与控制, 2020, 9(4): 185-195.
[22] 范蓉, 王为群, 姚娟. 一类时变时滞不确定离散系统的预见跟踪控制[J]. 动力系统与控制, 2018, 7(3): 201-213.

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