IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v321y2018icp450-462.html
   My bibliography  Save this article

L2−L∞ synchronization for singularly perturbed complex networks with semi-Markov jump topology

Author

Listed:
  • Liang, Kun
  • Dai, Mingcheng
  • Shen, Hao
  • Wang, Jing
  • Wang, Zhen
  • Chen, Bo

Abstract

This paper is concerned with the problem of L2--L∞ synchronization for singularly perturbed complex networks (SPCNs) with semi-Markov jump topology, in which the phenomenon of the singular perturbation is fully taken into consideration. The topology of complex dynamical network is time-varying switching regulated by the semi-Markov jump mechanism. The priority of this work is to obtain some conditions which ensure the underlying complex dynamical network (CDN) is stochastically synchronized with a stated L2--L∞ performance level. Based on Lyapunov method and convex optimization technique, the synchronization conditions can be obtained via solving convex optimization problems. Finally, the correctness and validity of our proposed synchronization method are well demonstrated by a simulation example.

Suggested Citation

  • Liang, Kun & Dai, Mingcheng & Shen, Hao & Wang, Jing & Wang, Zhen & Chen, Bo, 2018. "L2−L∞ synchronization for singularly perturbed complex networks with semi-Markov jump topology," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 450-462.
    • Handle: RePEc:eee:apmaco:v:321:y:2018:i:c:p:450-462
    DOI: 10.1016/j.amc.2017.10.039
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300317307385
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2017.10.039?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Zhou, Jiamu & Dong, Hailing & Feng, Jianwen, 2017. "Event-triggered communication for synchronization of Markovian jump delayed complex networks with partially unknown transition rates," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 617-629.
    2. Su, Lei & Shen, Hao, 2015. "Mixed H∞/passive synchronization for complex dynamical networks with sampled-data control," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 931-942.
    3. Song, Xiaona & Men, Yunzhe & Zhou, Jianping & Zhao, Junjie & Shen, Hao, 2017. "Event-triggered H∞ control for networked discrete-time Markov jump systems with repeated scalar nonlinearities," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 123-132.
    4. Sivaranjani, K. & Rakkiyappan, R. & Cao, Jinde & Alsaedi, Ahmed, 2017. "Synchronization of nonlinear singularly perturbed complex networks with uncertain inner coupling via event triggered control," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 283-299.
    5. Shen, Mouquan & Yan, Shen & Zhang, Guangming & Park, Ju H., 2016. "Finite-time H∞ static output control of Markov jump systems with an auxiliary approach," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 553-561.
    6. Li, Feng & Shen, Hao & Chen, Mengshen & Kong, Qingkai, 2015. "Non-fragile finite-time l2−l∞ state estimation for discrete-time Markov jump neural networks with unreliable communication links," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 467-481.
    7. Jin, Yunguo & Zhong, Shouming, 2015. "Function projective synchronization in complex networks with switching topology and stochastic effects," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 730-740.
    8. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    9. Chen, Mengshen & Yang, Xiaofei & Shen, Hao & Yao, Fengqi, 2016. "Finite-time asynchronous H∞ control for Markov jump repeated scalar non-linear systems with input constraints," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 172-180.
    10. Xu, Ruiping & Kao, Yonggui & Gao, Cunchen, 2015. "Exponential synchronization of delayed Markovian jump complex networks with generally uncertain transition rates," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 682-693.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yu, Peng & Ma, Yuechao, 2020. "Observer-based asynchronous control for Markov jump systems," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    2. Fan, Ming-Can & Wu, Yue, 2018. "Global leader-following consensus of nonlinear multi-agent systems with unknown control directions and unknown external disturbances," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 274-286.
    3. Li, Li & Wang, Zhen & Li, Yuxia & Shen, Hao & Lu, Junwei, 2018. "Hopf bifurcation analysis of a complex-valued neural network model with discrete and distributed delays," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 152-169.
    4. Ziye Zhang & Xiaoping Liu & Chong Lin & Bing Chen, 2018. "Finite-Time Synchronization for Complex-Valued Recurrent Neural Networks with Time Delays," Complexity, Hindawi, vol. 2018, pages 1-14, December.
    5. Jiao, Shiyu & Shen, Hao & Wei, Yunliang & Huang, Xia & Wang, Zhen, 2018. "Further results on dissipativity and stability analysis of Markov jump generalized neural networks with time-varying interval delays," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 338-350.
    6. Li, Yankai & Chen, Mou & Li, Tao & Shi, Peng, 2020. "Anti-disturbance reference mode resilient dynamic output feedback control for turbofan systems," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    7. Wang, Jing & Ru, Tingting & Xia, Jianwei & Wei, Yunliang & Wang, Zhen, 2019. "Finite-time synchronization for complex dynamic networks with semi-Markov switching topologies: An H∞ event-triggered control scheme," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 235-251.
    8. Wang, Yao & Guo, Jun & Liu, Guobao & Lu, Junwei & Li, Fangyuan, 2021. "Finite-time sampled-data synchronization for uncertain neutral-type semi-Markovian jump neural networks with mixed time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    9. Long, Shaohua & Wu, Yunlong & Zhong, Shouming & Zhang, Dian, 2018. "Stability analysis for a class of neutral type singular systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 113-131.
    10. Zhuang, Guangming & Xu, Shengyuan & Xia, Jianwei & Ma, Qian & Zhang, Zhengqiang, 2019. "Non-fragile delay feedback control for neutral stochastic Markovian jump systems with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 21-32.
    11. Guo, Beibei & Xiao, Yu & Zhang, Chiping & Zhao, Yong, 2020. "Graph theory-based adaptive intermittent synchronization for stochastic delayed complex networks with semi-Markov jump," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    12. Rathinasamy Sakthivel & Ramalingam Sakthivel & Boomipalagan Kaviarasan & Chao Wang & Yong-Ki Ma, 2018. "Finite-Time Nonfragile Synchronization of Stochastic Complex Dynamical Networks with Semi-Markov Switching Outer Coupling," Complexity, Hindawi, vol. 2018, pages 1-13, January.
    13. Fan, Gaofeng & Ma, Yuechao, 2023. "Fault-tolerant fixed/preassigned-time synchronization control of uncertain singularly perturbed complex networks with time-varying delay and stochastic disturbances," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    14. Tan, Lihua & Li, Chuandong & Huang, Junjian & Huang, Tingwen, 2021. "Output feedback leader-following consensus for nonlinear stochastic multiagent systems: The event-triggered method," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    15. Tai, Weipeng & Teng, Qingyong & Zhou, Youmei & Zhou, Jianping & Wang, Zhen, 2019. "Chaos synchronization of stochastic reaction-diffusion time-delay neural networks via non-fragile output-feedback control," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 115-127.
    16. Wang, Jing & Liang, Kun & Huang, Xia & Wang, Zhen & Shen, Hao, 2018. "Dissipative fault-tolerant control for nonlinear singular perturbed systems with Markov jumping parameters based on slow state feedback," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 247-262.
    17. Yangjie Chen & Fan Zhang & Jianning Li, 2022. "Anti-Disturbance Fault-Tolerant Constrained Consensus for Time-Delay Faulty Multi-Agent Systems with Semi-Markov Switching Topology," Mathematics, MDPI, vol. 10(23), pages 1-17, December.
    18. Huang, Xin & Liu, Yamin & Wang, Yang & Zhou, Jianping & Fang, Muyun & Wang, Zhen, 2020. "L2−L∞ consensus of stochastic delayed multi-agent systems with ADT switching interaction topologies," Applied Mathematics and Computation, Elsevier, vol. 368(C).
    19. Jiao, Ticao & Park, Ju H. & Zong, Guangdeng & Liu, Jian & Chen, Yu, 2019. "Stochastic stability analysis of switched genetic regulatory networks without stable subsystems," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 261-277.
    20. Yang, Te & Chen, Guoliang & Xia, Jianwei & Wang, Zhen & Sun, Qun, 2019. "Robust H∞ filtering for polytopic uncertain stochastic systems under quantized sampled outputs," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 688-701.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ye, Dan & Yang, Xiang & Su, Lei, 2017. "Fault-tolerant synchronization control for complex dynamical networks with semi-Markov jump topology," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 36-48.
    2. Song, Xiaona & Men, Yunzhe & Zhou, Jianping & Zhao, Junjie & Shen, Hao, 2017. "Event-triggered H∞ control for networked discrete-time Markov jump systems with repeated scalar nonlinearities," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 123-132.
    3. Gao, Xianwen & He, Hangfeng & Qi, Wenhai, 2017. "Admissibility analysis for discrete-time singular Markov jump systems with asynchronous switching," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 431-441.
    4. Li, Qiaoping & Liu, Sanyang & Chen, Yonggang, 2018. "Combination event-triggered adaptive networked synchronization communication for nonlinear uncertain fractional-order chaotic systems," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 521-535.
    5. Luo, Mengzhuo & Liu, Xinzhi & Zhong, Shouming & Cheng, Jun, 2018. "Synchronization of multi-stochastic-link complex networks via aperiodically intermittent control with two different switched periods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 20-38.
    6. Luo, Jinnan & Tian, Wenhong & Zhong, Shouming & Shi, Kaibo & Chen, Hao & Gu, Xian-Ming & Wang, Wenqin, 2017. "Non-fragile asynchronous H∞ control for uncertain stochastic memory systems with Bernoulli distribution," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 109-128.
    7. Wang, Jing & Liang, Kun & Huang, Xia & Wang, Zhen & Shen, Hao, 2018. "Dissipative fault-tolerant control for nonlinear singular perturbed systems with Markov jumping parameters based on slow state feedback," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 247-262.
    8. Jiao, Shiyu & Shen, Hao & Wei, Yunliang & Huang, Xia & Wang, Zhen, 2018. "Further results on dissipativity and stability analysis of Markov jump generalized neural networks with time-varying interval delays," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 338-350.
    9. Fu, Lei & Ma, Yuechao, 2016. "Passive control for singular time-delay system with actuator saturation," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 181-193.
    10. Fei Wang & Zhaowen Zheng & Yongqing Yang, 2019. "Synchronization of Complex Dynamical Networks with Hybrid Time Delay under Event-Triggered Control: The Threshold Function Method," Complexity, Hindawi, vol. 2019, pages 1-17, December.
    11. Fang, Liandi & Ma, Li & Ding, Shihong & Zhao, Dean, 2019. "Finite-time stabilization for a class of high-order stochastic nonlinear systems with an output constraint," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 63-79.
    12. Zhai, Ding & Lu, An-Yang & Dong, Jiuxiang & Zhang, Qing-Ling, 2016. "Asynchronous H∞ filtering for 2D discrete Markovian jump systems with sensor failure," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 60-79.
    13. Aravindh, D. & Sakthivel, R. & Kong, Fanchao & Marshal Anthoni, S., 2020. "Finite-time reliable stabilization of uncertain semi-Markovian jump systems with input saturation," Applied Mathematics and Computation, Elsevier, vol. 384(C).
    14. Yao, Xiuming & Lian, Yue & Park, Ju H., 2019. "Disturbance-observer-based event-triggered control for semi-Markovian jump nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    15. Kwon, Nam Kyu & Park, In Seok & Park, PooGyeon, 2017. "H∞ control for singular Markovian jump systems with incomplete knowledge of transition probabilities," Applied Mathematics and Computation, Elsevier, vol. 295(C), pages 126-135.
    16. Zhang, Ruimei & Zeng, Deqiang & Zhong, Shouming & Yu, Yongbin, 2017. "Event-triggered sampling control for stability and stabilization of memristive neural networks with communication delays," Applied Mathematics and Computation, Elsevier, vol. 310(C), pages 57-74.
    17. Emerson, Isaac Arnold & Amala, Arumugam, 2017. "Protein contact maps: A binary depiction of protein 3D structures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 782-791.
    18. Li, Chengren & Lü, Ling & Li, Gang & Zhao, Guannan & Gao, Liyu & Ge, Lianjun & Han, Changhui, 2019. "Cluster synchronization in uncertain network with nonidentical nodes based on adaptive pinning control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 742-749.
    19. Ruiz Vargas, E. & Mitchell, D.G.V. & Greening, S.G. & Wahl, L.M., 2014. "Topology of whole-brain functional MRI networks: Improving the truncated scale-free model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 151-158.
    20. Igor Belykh & Mateusz Bocian & Alan R. Champneys & Kevin Daley & Russell Jeter & John H. G. Macdonald & Allan McRobie, 2021. "Emergence of the London Millennium Bridge instability without synchronisation," Nature Communications, Nature, vol. 12(1), pages 1-14, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:321:y:2018:i:c:p:450-462. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.