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Finite-time stability and stabilisation for a class of nonlinear systems with time-varying delay

Author

Listed:
  • Hao Liu
  • Peng Shi
  • Hamid Reza Karimi
  • Mohammed Chadli

Abstract

This paper is concerned with the problems of finite-time stability (FTS) and finite-time stabilisation for a class of nonlinear systems with time-varying delay, which can be represented by Takagi–Sugeno fuzzy system. Some new delay-dependent FTS conditions are provided and applied to the design problem of finite-time fuzzy controllers. First, based on an integral inequality and a fuzzy Lyapunov–Krasovskii functional, a delay-dependent FTS criterion is proposed for open-loop fuzzy system by introducing some free fuzzy weighting matrices, which are less conservative than other existing ones. Then, the parallel distributed compensation controller is designed to ensure FTS of the time-delay fuzzy system. Finally, an example is given to illustrate the effectiveness of the proposed design approach.

Suggested Citation

  • Hao Liu & Peng Shi & Hamid Reza Karimi & Mohammed Chadli, 2016. "Finite-time stability and stabilisation for a class of nonlinear systems with time-varying delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(6), pages 1433-1444, April.
    • Handle: RePEc:taf:tsysxx:v:47:y:2016:i:6:p:1433-1444
    DOI: 10.1080/00207721.2014.932467
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    Cited by:

    1. Fu, Xiaozheng & Zhu, Quanxin, 2020. "Exponential stability of neutral stochastic delay differential equation with delay-dependent impulses," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    2. Harshavarthini, S. & Sakthivel, R. & Kong, F., 2020. "Finite-time synchronization of chaotic coronary artery system with input time-varying delay," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    3. Sakthivel, R. & Joby, Maya & Wang, Chao & Kaviarasan, B., 2018. "Finite-time fault-tolerant control of neutral systems against actuator saturation and nonlinear actuator faults," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 425-436.
    4. Harshavarthini, S. & Sakthivel, R. & Ma, Yong-Ki & Muslim, M., 2020. "Finite-time resilient fault-tolerant investment policy scheme for chaotic nonlinear finance system," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    5. Wu, Kai-Ning & Na, Ming-Ye & Wang, Liming & Ding, Xiaohua & Wu, Boying, 2019. "Finite-time stability of impulsive reaction-diffusion systems with and without time delay," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    6. Tharanidharan, V. & Sakthivel, R. & Ren, Yong & Marshal Anthoni, S., 2022. "Robust finite-time PID control for discrete-time large-scale interconnected uncertain system with discrete-delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 370-383.
    7. 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).

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