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Finite-time stability and stabilization for Itô-type stochastic Markovian jump systems with generally uncertain transition rates

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  • Yan, Zhiguo
  • Song, Yunxia
  • Liu, Xiaoping

Abstract

This paper investigates the problems of finite-time stability and stabilization for stochastic Markovian jump systems with generally uncertain transition rates (SMJSwGUTRs). Firstly, a less conservative stability criterion is presented by a mode-dependent approach. Then, the state feedback controller and observer-based controller are designed by a cone complementary linearization method, and two specific algorithms are presented. Finally, an example is used to illustrate our results.

Suggested Citation

  • Yan, Zhiguo & Song, Yunxia & Liu, Xiaoping, 2018. "Finite-time stability and stabilization for Itô-type stochastic Markovian jump systems with generally uncertain transition rates," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 512-525.
    • Handle: RePEc:eee:apmaco:v:321:y:2018:i:c:p:512-525
    DOI: 10.1016/j.amc.2017.10.049
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    References listed on IDEAS

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    1. Yonggui Kao & Changhong Wang & Jing Xie & Hamid Reza Karimi, 2016. "New delay-dependent stability of Markovian jump neutral stochastic systems with general unknown transition rates," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(11), pages 2499-2509, August.
    2. Hien, Le Van & Son, Doan Thai, 2015. "Finite-time stability of a class of non-autonomous neural networks with heterogeneous proportional delays," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 14-23.
    3. Su, Qingyu & Jia, Xiaolong & Liu, Honghai, 2016. "Finite-time stabilization of a class of cascade nonlinear switched systems under state-dependent switching," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 172-180.
    4. Ma, Yuechao & Jia, Xiaorui & Liu, Deyou, 2016. "Robust finite-time H∞ control for discrete-time singular Markovian jump systems with time-varying delay and actuator saturation," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 213-227.
    5. 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.
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    Cited by:

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    2. Xiao, Xiaoqing & Park, Ju H. & Zhou, Lei, 2018. "Event-triggered control of discrete-time switched linear systems with packet losses," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 344-352.
    3. Guo, Beibei & Wu, Yinhu & Xiao, Yu & Zhang, Chiping, 2018. "Graph-theoretic approach to synchronizing stochastic coupled systems with time-varying delays on networks via periodically intermittent control," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 341-357.
    4. Xikui Liu & Wencong Li & Chenxin Yao & Yan Li, 2022. "Finite-Time Guaranteed Cost Control for Markovian Jump Systems with Time-Varying Delays," Mathematics, MDPI, vol. 10(12), pages 1-12, June.
    5. Yan, Zhiguo & Zhang, Min & Chang, Gaizhen & Lv, Hui & Park, Ju H., 2022. "Finite-time annular domain stability and stabilization of Itô stochastic systems with Wiener noise and Poisson jumps-differential Gronwall inequality approach," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    6. Ren, Yuanhong & Wang, Weiqun & Wang, Yixiang, 2018. "Incremental H∞ control for switched nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 251-263.
    7. Gaizhen Chang & Tingkun Sun & Zhiguo Yan & Min Zhang & Xiaomin Zhou, 2022. "Quantitative Mean Square Exponential Stability and Stabilization of Linear Itô Stochastic Markovian Jump Systems Driven by Both Brownian and Poisson Noises," Mathematics, MDPI, vol. 10(13), pages 1-16, July.
    8. Zhang, Huanjun & Yan, Zhiguo, 2020. "Backward stochastic optimal control with mixed deterministic controller and random controller and its applications in linear-quadratic control," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    9. Guo, Ying & Zhao, Wei & Ding, Xiaohua, 2019. "Input-to-state stability for stochastic multi-group models with multi-dispersal and time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 114-127.
    10. Zhao, Yinghong & Ma, Yuechao, 2021. "Asynchronous H∞ control for hidden singular Markov jump systems with incomplete transition probabilities via state decomposition approach," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    11. Zhang, Jianan & Ma, Yuechao, 2023. "Adaptive fault-tolerant double asynchronous control for switched semi-Markov jump systems via improved memory sampled-data technique," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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