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LMIs-based exponential stabilization for interval delay systems via congruence transformation: Application in chaotic Lorenz system

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  • Zheng, Wei
  • Zhang, Zhiming
  • Lam, Hak-Keung
  • Sun, Fuchun
  • Wen, Shuhuan

Abstract

This paper investigates the stochastic Takagi-Sugeno (T-S) fuzzy uncertainty-dependent state feedback sampled-data control, asymptotical stability and exponential stability analysis for a class of stochastic T-S fuzzy system with measurable uncertainties, mixed interval time varying delays and Gaussian white noise. Firstly, the T-S fuzzy model and stochastic Bernoulli theory are employed to approximate the system plant. Secondly, the stochastic T-S fuzzy uncertainty-dependent state feedback sampled-data controller is designed via uncertainty-dependent parameters and the hold times series of sampled-data. Thirdly, the Bernoulli probability distribution is employed to describe the random occurrence characteristic of multipath packet dropouts. Three classes of delay-dependent stability conditions in terms of linear matrix inequalities (LMIs) are derived for the closed-loop system. The multiple integral fuzzy-basis-dependent Lyapunov functional and augmented state variable are employed to derive the delay-dependent stability conditions, then the closed-loop system is asymptotically stable and exponentially stable. The congruence transformation method and prescribed H-infinity performance functional are employed to derive the less conservative delay-dependent stability conditions, and the prescribed H-infinity performance is guaranteed. The relaxation matrix and congruence transformation method are employed to design the linear transformation equalities and congruence transformation matrices, then the controller gain matrix is determined and computation complexity of solving LMIs is reduced. Finally, the proposed method is applied in the chaotic Lorenz system to show the effectiveness and advantage of proposed method.

Suggested Citation

  • Zheng, Wei & Zhang, Zhiming & Lam, Hak-Keung & Sun, Fuchun & Wen, Shuhuan, 2023. "LMIs-based exponential stabilization for interval delay systems via congruence transformation: Application in chaotic Lorenz system," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    • Handle: RePEc:eee:chsofr:v:176:y:2023:i:c:s096007792300961x
    DOI: 10.1016/j.chaos.2023.114060
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    References listed on IDEAS

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    1. Zhang, Meng & Zhu, Quanxin, 2022. "Finite-time input-to-state stability of switched stochastic time-varying nonlinear systems with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    2. You, Xingxing & Shi, Mingyang & Guo, Bin & Zhu, Yuqi & Lai, Wuxing & Dian, Songyi & Liu, Kai, 2022. "Event-triggered adaptive fuzzy tracking control for a class of fractional-order uncertain nonlinear systems with external disturbance," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    3. Li, Xueling & Lin, Xiangze & Zou, Yun, 2021. "Finite-time stabilization of high-order output-constrained switched systems via state feedback," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    4. Dong, Zeyu & Wang, Xin & Zhang, Xian, 2020. "A nonsingular M-matrix-based global exponential stability analysis of higher-order delayed discrete-time Cohen–Grossberg neural networks," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    5. Zhang, Zhiming & Zheng, Wei & Lam, H.K. & Wen, Shuhuan & Sun, Fuchun & Xie, Ping, 2020. "Stability analysis and output feedback control for stochastic networked systems with multiple communication delays and nonlinearities using fuzzy control technique," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    6. Thoiyab, N. Mohamed & Muruganantham, P. & Zhu, Quanxin & Gunasekaran, Nallappan, 2021. "Novel results on global stability analysis for multiple time-delayed BAM neural networks under parameter uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    7. Zhong, Yuguang & Song, Dening, 2023. "Nonfragile synchronization control of T-S fuzzy Markovian jump complex dynamical networks," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    8. Liu, Xiang & Wang, Peiguang & Anderson, Douglas R., 2022. "On stability and feedback control of discrete fractional order singular systems with multiple time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    9. Shen, Shiping & Meng, Xiaofang, 2023. "Finite-time stability of almost periodic solutions of Clifford-valued RNNs with time-varying delays and D operator on time scales," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    10. Peng, Shuo & Wang, Qingzhi & Fu, Baozeng, 2022. "Exponential stabilization of chaotic systems based on fuzzy time-triggered intermittent control," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    11. Baoyu Huo & Shaocheng Tong & Yongming Li, 2013. "Adaptive fuzzy fault-tolerant output feedback control of uncertain nonlinear systems with actuator faults," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(12), pages 2365-2376.
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    Cited by:

    1. Cheng, Guifang & Liu, Hao, 2024. "Asynchronous finite-time extended dissipative sliding mode control for semi-Markovian jump master–slave neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).

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