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Leveraging an LMI‐Based Approach for Finite‐Time Control of Nonlinear Systems in the Presence of State‐Dependent Delays and Parametric Uncertainties

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  • Elahe Moradi

Abstract

In recent years, the study of finite‐time stability (FTS) and finite‐time control (FTC) of time‐delay systems has attracted significant attention from researchers. This article investigates the problems of FTS and FTC for nonlinear systems in the presence of state‐dependent delays and parametric uncertainties. The considered delay is time‐varying, and the nonlinear system is assumed to satisfy the Lipschitz condition. First, sufficient conditions for ensuring FTS of the nonlinear time‐delay system with parametric uncertainties are derived in the framework of linear matrix inequalities (LMIs). Next, LMI‐based sufficient conditions are established for guaranteeing FTC via modified state‐feedback control. The obtained FTS and FTC conditions are delay‐dependent, providing a more precise characterization of the system’s transient behavior. To establish the theoretical results, the Newton–Leibniz formula and a Lyapunov–Krasovskii functional (LKF) candidate were employed. Finally, the effectiveness of the proposed approach is demonstrated through two illustrative examples and corresponding MATLAB simulations.

Suggested Citation

  • Elahe Moradi, 2025. "Leveraging an LMI‐Based Approach for Finite‐Time Control of Nonlinear Systems in the Presence of State‐Dependent Delays and Parametric Uncertainties," Complexity, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:complx:v:2025:y:2025:i:1:n:6370708
    DOI: 10.1155/cplx/6370708
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    References listed on IDEAS

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    1. Shanmugam Saravanan & M. Syed Ali & Grienggrai Rajchakit & Bussakorn Hammachukiattikul & Bandana Priya & Ganesh Kumar Thakur & Jianquan Lu, 2021. "Finite-Time Stability Analysis of Switched Genetic Regulatory Networks with Time-Varying Delays via Wirtinger’s Integral Inequality," Complexity, Hindawi, vol. 2021, pages 1-21, January.
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    3. Nima Maleki & Elahe Moradi, 2022. "Robust H∞ Control of DC Motor in the Presence of Input Delay and Disturbance by the Predictor‐Based Method," Complexity, John Wiley & Sons, vol. 2022(1).
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    5. Honglei Xu, 2020. "Finite-Time Stability Analysis: A Tutorial Survey," Complexity, Hindawi, vol. 2020, pages 1-12, October.
    6. Nima Maleki & Elahe Moradi & Mohammad Hassan Khooban, 2022. "Robust H∞ Control of DC Motor in the Presence of Input Delay and Disturbance by the Predictor-Based Method," Complexity, Hindawi, vol. 2022, pages 1-10, November.
    7. Qiangqiang Zhu & Ben Niu & Shengtao Li & Peiyong Duan & Dong Yang, 2020. "Finite-Time Adaptive Tracking Control for a Class of Pure-Feedback Nonlinear Systems with Disturbances via Decoupling Technique," Complexity, Hindawi, vol. 2020, pages 1-11, August.
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