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Robust finite-time stabilization for positive delayed semi-Markovian switching systems

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  • Qi, Wenhai
  • Zong, Guangdeng
  • Cheng, Jun
  • Jiao, Ticao

Abstract

Robust finite-time stabilization is discussed for positive semi-Markovian switching systems (S-MSSs), in which semi-Markovian process, time-varying delay, external disturbance, and transient performance in finite-time level are all considered in a unified framework. In the system under consideration, finite-time problem can describe transient performance of practical control process. Firstly, some finite-time boundedness and L1 finite-time boundedness criteria for positive delayed S-MSSs are proposed by constructing the stochastic semi-Markovian Lyapunov–Krasovskii functional with mode-dependent integral term. Then, a developed L1 finite-time feedback controller design method is presented to reduce some constraints of input matrices, which guarantees the resulting closed-loop system achieves positivity, finite-time boundedness, and has a prescribed L1 noise attenuation performance index in a novel standard linear programming. Finally, a practical example is illustrated to validate the proposed results by applying a virus mutation treatment model.

Suggested Citation

  • Qi, Wenhai & Zong, Guangdeng & Cheng, Jun & Jiao, Ticao, 2019. "Robust finite-time stabilization for positive delayed semi-Markovian switching systems," Applied Mathematics and Computation, Elsevier, vol. 351(C), pages 139-152.
    • Handle: RePEc:eee:apmaco:v:351:y:2019:i:c:p:139-152
    DOI: 10.1016/j.amc.2018.12.069
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    References listed on IDEAS

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    1. Chen, Xiaoming & Chen, Mou & Qi, Wenhai & Shen, Jun, 2016. "Dynamic output-feedback control for continuous-time interval positive systems under L1 performance," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 48-59.
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    5. Xudong Zhao & Yunfei Yin & Jun Shen, 2016. "Reset stabilisation of positive linear systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(12), pages 2773-2782, September.
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    Cited by:

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    2. Zhang, Lihua & Zhou, Yaoyao & Qi, Wenhai & Cao, Jinde & Cheng, Jun & Wei, Yunliang & Yan, Xiaoyu & Li, Shaowu, 2020. "Non-fragile observer-based H∞ finite-time sliding mode control," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    3. Yao, Hejun & Gao, Fangzheng & Huang, Jiacai & Wu, Yuqiang, 2021. "Global prescribed-time stabilization via time-scale transformation for switched nonlinear systems subject to switching rational powers," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    4. Wang, Jinling & Liang, Jinling & Zhang, Cheng-Tang & Fan, Dongmei, 2021. "Event-triggered non-fragile control for uncertain positive Roesser model with PDT switching mechanism," Applied Mathematics and Computation, Elsevier, vol. 406(C).
    5. Li, Shuo & Xiang, Zhengrong, 2020. "Positivity, exponential stability and disturbance attenuation performance for singular switched positive systems with time-varying distributed delays," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    6. Li, Zhao-Yan & Shang, Shengnan & Lam, James, 2019. "On stability of neutral-type linear stochastic time-delay systems with three different delays," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 147-166.
    7. Du, Haibo & Yu, Bo & Wei, Jiajia & Zhang, Jun & Wu, Di & Tao, Weiqing, 2020. "Attitude trajectory planning and attitude control for quad-rotor aircraft based on finite-time control technique," Applied Mathematics and Computation, Elsevier, vol. 386(C).

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