Zuoping Zhao1This email address is being protected from spambots. You need JavaScript enabled to view it., Dongyang Li2, and Zhengjian Lai3
1College of Engineering, Yanbian University, Yanji, 133002, China
2Technology Center, Nanyang Beifangxiangdong Industrial Co., Ltd., Nanyang, 474677, China
3College of Automotive Technology, Sichuan Vocational and Technical College, Suining, 629099, China
Received: April 17, 2025 Accepted: June 25, 2025 Publication Date: August 16, 2025
Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.
The chattering phenomenon is a problem in sliding mode technique under discrete-time implementation. In this paper, a novel discrete-time algorithm for the hybrid non-homogeneous sliding mode differentiator is presented to prevent chattering in output signals. To be specific, an equivalence framework is employed linking the traditional set-valued signum function with the multilayer set-valued mapping to reduce discretization complexity. The stability of the system is analyzed using a combined Lyapunov approach and input-to-state stability theory. In addition, the discretization procedure is based on the equivalence relation between the set-valued function and the saturation function, as well as the implicit-Euler method. Numerical simulations demonstrate that the proposed algorithm completely suppresses chattering (0 amplitude), outperforming both the sigmoid function method (2.5×10−7 amplitude) and the boundary layer method (2.0×10−7 amplitude), while achieving improved filtering performance and enhanced disturbance rejection, thereby yielding more reliable output signals.
Keywords: chattering phenomenon; sliding mode; signum fuction; implicit-Euler
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