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Volume 12 Issue 11
Nov.  2025

IEEE/CAA Journal of Automatica Sinica

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Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2025  >  12(11): 2264-2274
X. Liu and Z. Wang, “Optimal Lyapunov function and minimum amplitude control for disturbed linear systems,” IEEE/CAA J. Autom. Sinica, vol. 12, no. 11, pp. 2264–2274, Nov. 2025. doi: 10.1109/JAS.2025.125252
Citation: X. Liu and Z. Wang, “Optimal Lyapunov function and minimum amplitude control for disturbed linear systems,” IEEE/CAA J. Autom. Sinica, vol. 12, no. 11, pp. 2264–2274, Nov. 2025. doi: 10.1109/JAS.2025.125252
shu

Optimal Lyapunov Function and Minimum Amplitude Control for Disturbed Linear Systems

doi: 10.1109/JAS.2025.125252
Funds:  This work was supported in part by the National Natural Science Foundation of China (62373089)
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    Abstract
  • It is a challenging issue to obtain the minimum amplitude control for linear systems subject to amplitude-bounded disturbances. The difficulty is how to accurately give the quantitative relationship between the system H∞ norm and control parameters. An optimal-Lyapunov-function-based controller design concept is proposed, and a minimum amplitude control scheme is presented under amplitude-bounded disturbances. Firstly, the optimal Lyapunov function is proposed by analyzing the geometric characteristics of the system H∞ norm, and the necessary and sufficient condition of the optimal Lyapunov function parameter matrix is given. Secondly, the optimal Lyapunov function parameter matrix is constructed in the parameterized matrix equation, and the accurate quantitative relationship between the system H∞ norm and control parameters is given. Finally, the control parameter optimization method is proposed according to the quantitative relationship between the system H∞ norm and control parameters. Unlike robust optimization control methods, the presented minimum amplitude control scheme avoids the improper selection of the Lyapunov function in the controller design, and provides a novel way to design the minimum amplitude control under the given control accuracy. A buck converter example is given to illustrate the effectiveness and practicability of the presented scheme.

     

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