IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v342y2019icp191-205.html
   My bibliography  Save this article

A flexible terminal approach to stochastic stability and stabilization of continuous-time semi-Markovian jump systems with time-varying delay

Author

Listed:
  • Zhang, Dian
  • Cheng, Jun
  • Ki Ahn, Choon
  • Ni, Hongjie

Abstract

This paper addresses the stochastic stability and stabilization problems for a class of semi-Markovian jump systems (SMJSs) with time-varying delay, where the time-varying delay τ(t) is assumed to satisfy τ1 ≤ τ(t) ≤ τ2. Based on the flexible terminal approach, the time-varying delay τ(t) is first transformed such that τ1(t) ≤ τ(t) ≤ τ2(t). By utilizing a novel semi-Markovian Lyapunov Krasoviskii functional (SMLKF) and an improved reciprocally convex inequality (RCI), sufficient conditions are established to guarantee a feasible solution. Two illustrated examples are shown the effectiveness of the main results.

Suggested Citation

  • Zhang, Dian & Cheng, Jun & Ki Ahn, Choon & Ni, Hongjie, 2019. "A flexible terminal approach to stochastic stability and stabilization of continuous-time semi-Markovian jump systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 191-205.
  • Handle: RePEc:eee:apmaco:v:342:y:2019:i:c:p:191-205
    DOI: 10.1016/j.amc.2018.09.035
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318308130
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2018.09.035?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. 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.
    2. Ge, Chao & Wang, Bingfang & Wei, Xian & Liu, Yajuan, 2017. "Exponential synchronization of a class of neural networks with sampled-data control," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 150-161.
    3. Renquan Lu & Bin Lou & An-Ke Xue, 2015. "Mode-dependent quantised filtering for Markovian jump singular system," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(10), pages 1817-1824, July.
    4. Guo, Runan & Zhang, Ziye & Liu, Xiaoping & Lin, Chong, 2017. "Existence, uniqueness, and exponential stability analysis for complex-valued memristor-based BAM neural networks with time delays," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 100-117.
    5. Wang, Bo & Yan, Juan & Cheng, Jun & Zhong, Shouming, 2017. "New criteria of stability analysis for generalized neural networks subject to time-varying delayed signals," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 322-333.
    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. Nguyen, Ngoc Hoai An & Kim, Sung Hyun, 2021. "Asynchronous dissipative control design for semi-Markovian jump systems with uncertain probability distribution functions of sojourn-time," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    2. Lin, Yuqian & Zhuang, Guangming & Sun, Wei & Zhao, Junsheng & Chu, Yuming, 2021. "Resilient H∞ dynamic output feedback controller design for USJSs with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    3. Zhang, Huasheng & Zhuang, Guangming & Sun, Wei & Li, Yongmin & Lu, Junwei, 2020. "pth moment asymptotic interval stability and stabilization of linear stochastic systems via generalized H-representation," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    4. Zhang, Dian & Cheng, Jun & Cao, Jinde & Zhang, Dan, 2019. "Finite-time synchronization control for semi-Markov jump neural networks with mode-dependent stochastic parametric uncertainties," Applied Mathematics and Computation, Elsevier, vol. 344, pages 230-242.

    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. 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.
    2. Yueping Sun & Li Ma & Dean Zhao & Shihong Ding, 2018. "A Compound Controller Design for a Buck Converter," Energies, MDPI, vol. 11(9), pages 1-17, September.
    3. Xie, Wenqian & Zhu, Hong & Zhong, Shouming & Zhang, Dian & Shi, Kaibo & Cheng, Jun, 2018. "Extended dissipative estimator design for uncertain switched delayed neural networks via a novel triple integral inequality," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 82-102.
    4. Wang, Jun & Shi, Kaibo & Huang, Qinzhen & Zhong, Shouming & Zhang, Dian, 2018. "Stochastic switched sampled-data control for synchronization of delayed chaotic neural networks with packet dropout," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 211-230.
    5. Shan, Yaonan & She, Kun & Zhong, Shouming & Zhong, Qishui & Shi, Kaibo & Zhao, Can, 2018. "Exponential stability and extended dissipativity criteria for generalized discrete-time neural networks with additive time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 145-168.
    6. Shi, Kaibo & Wang, Jun & Zhong, Shouming & Zhang, Xiaojun & Liu, Yajuan & Cheng, Jun, 2019. "New reliable nonuniform sampling control for uncertain chaotic neural networks under Markov switching topologies," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 169-193.
    7. Zeng, Deqiang & Zhang, Ruimei & Liu, Xinzhi & Zhong, Shouming & Shi, Kaibo, 2018. "Pinning stochastic sampled-data control for exponential synchronization of directed complex dynamical networks with sampled-data communications," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 102-118.
    8. 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.
    9. Fu, Xiaozheng & Zhu, Quanxin & Guo, Yingxin, 2019. "Stabilization of stochastic functional differential systems with delayed impulses," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 776-789.
    10. Zhang, Kun & Zhang, Huaguang & Mu, Yunfei & Sun, Shaoxin, 2019. "Tracking control optimization scheme for a class of partially unknown fuzzy systems by using integral reinforcement learning architecture," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 344-356.
    11. R. Sakthivel & V. Nithya & Yong-Ki Ma & Chao Wang, 2018. "Finite-Time Nonfragile Dissipative Filter Design for Wireless Networked Systems with Sensor Failures," Complexity, Hindawi, vol. 2018, pages 1-13, October.
    12. Wang, Chen & Zhang, Hai & Ye, Renyu & Zhang, Weiwei & Zhang, Hongmei, 2023. "Finite time passivity analysis for Caputo fractional BAM reaction–diffusion delayed neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 424-443.
    13. Zhen Yang & Zhengqiu Zhang, 2022. "Finite-Time Synchronization Analysis for BAM Neural Networks with Time-Varying Delays by Applying the Maximum-Value Approach with New Inequalities," Mathematics, MDPI, vol. 10(5), pages 1-16, March.
    14. 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.
    15. Wang, Lingyu & Huang, Tingwen & Xiao, Qiang, 2018. "Global exponential synchronization of nonautonomous recurrent neural networks with time delays on time scales," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 263-275.
    16. Cao, Yang & Udhayakumar, K. & Veerakumari, K. Pradeepa & Rakkiyappan, R., 2022. "Memory sampled data control for switched-type neural networks and its application in image secure communications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 564-587.
    17. Li, Tao & Tang, Xiaoling & Qian, Wei & Fei, Shumin, 2019. "Hybrid-delay-dependent approach to synchronization in distributed delay neutral neural networks," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 449-463.
    18. Xia, ZeLiang & He, Shuping, 2022. "Finite-time asynchronous H∞ fault-tolerant control for nonlinear hidden markov jump systems with actuator and sensor faults," Applied Mathematics and Computation, Elsevier, vol. 428(C).
    19. Yang, Yi & Li, Xiaohua & Liu, Xiaoping, 2022. "Decentralized finite-time connective tracking control with prescribed settling time for p-normal form stochastic large-scale systems," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    20. Usa Humphries & Grienggrai Rajchakit & Pramet Kaewmesri & Pharunyou Chanthorn & Ramalingam Sriraman & Rajendran Samidurai & Chee Peng Lim, 2020. "Stochastic Memristive Quaternion-Valued Neural Networks with Time Delays: An Analysis on Mean Square Exponential Input-to-State Stability," Mathematics, MDPI, vol. 8(5), pages 1-26, May.

    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:342:y:2019:i:c:p:191-205. 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.