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Volume 13 Issue 9
Sep.  2026

IEEE/CAA Journal of Automatica Sinica

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Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2026  >  13(9): 2019-2027
H. Li, C. Hua, K. Li, and P. Ning, “Global prescribed-time control of nonlinear uncertain systems via a novel low-complexity analysis framework,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 9, pp. 2019–2027, Sep. 2026. doi: 10.1109/JAS.2025.125828
Citation: H. Li, C. Hua, K. Li, and P. Ning, “Global prescribed-time control of nonlinear uncertain systems via a novel low-complexity analysis framework,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 9, pp. 2019–2027, Sep. 2026. doi: 10.1109/JAS.2025.125828
shu

Global Prescribed-Time Control of Nonlinear Uncertain Systems via A Novel Low-Complexity Analysis Framework

doi: 10.1109/JAS.2025.125828
Funds:  This work was supported in part by the National Natural Science Foundation of China (U24A20271, U22A2050, and 62403183), the Science Fund of Hebei Province (F2023203100, F2020203013, and F2024208025), the Science and Technology Development Grant of Hebei Province (20311803D), the Hebei Innovation Capability Improvement Plan Project (22567619H), the S&T Program of Hebei (246Z1804G, 246Z1812G, 2024HBQZYCXY011, 242G1802Z, and 2023HBQZYCSB007), the Innovation Leading Talent Team Project at Higher Education Institutions of Hebei, the Key Research Projects in Fundamental Sciences at Higher Education Institutions of Hebei (241791007A), the Science Research Project of Hebei Education Department (CYZD202505), the Basic Operating Funds of Hebei University of Science and Technology (2023XLZ001), and the Guangxi Science and Technology Major Special Project (Guike AA22067064)
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    Abstract
  • The global prescribed-time stability problem of a class of uncertain systems is investigated. Utilizing the proposed ${\boldsymbol{\gamma}} $-fold convergence function, a novel low-complexity global prescribed-time stability analysis framework is developed. Existing virtual controllers based on time-varying transformation methods usually involve high-order derivative information of time-varying functions, posing significant challenges for stability analysis. We proposed a new stability criterion, which only involves the partial state variable on the right-hand side of the derivative inequality. The key advantage is that it eliminates the need for directly analyzing the boundedness of the virtual control gain coefficients with high-order time-varying functions. Building off this framework, we address the prescribed-time stabilization problem of multi-input multi-output (MIMO) nonlinear systems, where the Nussbaum gain function is extended to prescribed-time control to deal with time-varying sensor errors. Note that due to the infinitely divergent nature of time-varying functions at the terminal, ensuring the boundedness of the variables in the Nussbaum function is a challenge. Finally, we rigorously prove that all signals are bounded and the proposed controllers ensure that all state variables of systems converge to origin within a specified time, while the transient performance (convergence rate and specified overshoot) of the system output is also guaranteed. A simulation example is provided to illustrate the efficiency of the developed control algorithms.

     

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