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Practical stability of a nonlinear system with delayed control input

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Listed:
  • Zhang, He
  • Xu, Shengyuan
  • Zhang, Zhengqiang
  • Chu, Yuming

Abstract

The problem of delayed input control for a nonlinear system is discussed, where the nonlinearities of nonlinear systems are not assumed as Lipschitz continuous, they can be non-Lipschitz continuous or discontinuous in this paper. Notice that as a general nonlinear system, its sub-systems may have no common equilibrium or no equilibriums, but their trajectories may still be kept near equilibriums. Motivated by this, practical stability of nonlinear systems is considered by employing the Lyapuov method. Practical stability criteria in forms of linear matrix inequalities are obtained, where improved integral inequalities are given to reduce the conservatism of the obtained results. Finally, the obtained results are applied to analyze two problems of load frequency control of a one-area networked power system with sampled input and flight control of a two-degree-freedom helicopter system. The advantage and effectiveness of our approach are shown by a comparison with the literature.

Suggested Citation

  • Zhang, He & Xu, Shengyuan & Zhang, Zhengqiang & Chu, Yuming, 2022. "Practical stability of a nonlinear system with delayed control input," Applied Mathematics and Computation, Elsevier, vol. 423(C).
    • Handle: RePEc:eee:apmaco:v:423:y:2022:i:c:s0096300322000947
    DOI: 10.1016/j.amc.2022.127008
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    References listed on IDEAS

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    1. Zeng, Hong-Bing & Zhai, Zheng-Liang & Wang, Wei, 2021. "Hierarchical stability conditions of systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    2. Zhengqiang Zhang & Hao Shen & Ze Li & Shuzhen Zhang, 2015. "Zero-error tracking control of uncertain nonlinear systems in the presence of actuator hysteresis," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(15), pages 2853-2864, November.
    3. Liu, Wenhui & Lu, Junwei & Xu, Shengyuan & Li, Yongmin & Zhang, Zhengqiang, 2019. "Sampled-data controller design and stability analysis for nonlinear systems with input saturation and disturbances," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 14-27.
    4. Gao, Ming & Sheng, Li & Zhang, Weihai, 2015. "Stochastic H2/H∞ control of nonlinear systems with time-delay and state-dependent noise," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 429-440.
    5. Zeng, Hong-Bing & Zhai, Zheng-Liang & He, Yong & Teo, Kok-Lay & Wang, Wei, 2020. "New insights on stability of sampled-data systems with time-delay," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    6. Zeng, Hong-Bing & Liu, Xiao-Gui & Wang, Wei, 2019. "A generalized free-matrix-based integral inequality for stability analysis of time-varying delay systems," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 1-8.
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    Cited by:

    1. Shanmugam, Lakshmanan & Joo, Young Hoon, 2023. "Adaptive neural networks-based integral sliding mode control for T-S fuzzy model of delayed nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 450(C).
    2. Shenping Xiao & Jin Yu & Simon X. Yang & Yongfeng Qiu, 2022. "Stability Analysis for Time-Delay Systems via a New Negativity Condition on Quadratic Functions," Mathematics, MDPI, vol. 10(17), pages 1-9, August.

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