Exponential Convergence Analysis of Serial Differentiators for Robust and Accurate Estimation of High-Order Derivatives
This paper presents a rigorous mathematical analysis of the higher-order serial differentiator (HOSD), originally proposed by the authors for estimating time derivatives of time-varying signals. Unlike previous studies that partially relied on numerical simulations to demonstrate asymptotic converge...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
IEEE
2025-01-01
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| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/11005536/ |
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| Summary: | This paper presents a rigorous mathematical analysis of the higher-order serial differentiator (HOSD), originally proposed by the authors for estimating time derivatives of time-varying signals. Unlike previous studies that partially relied on numerical simulations to demonstrate asymptotic convergence of the estimation error, this work provides a complete analytical proof that both first- and higher-order derivative estimates converge exponentially fast to an arbitrarily small neighborhood of zero. Furthermore, it is analytically shown that replacing the discontinuous sign function in the differentiator dynamics with a smooth saturation function effectively mitigates chattering while preserving convergence to a small neighborhood around zero. The proposed analysis significantly strengthens the theoretical foundation of the HOSD and enhances its robustness and practical applicability in real-time control and estimation systems. |
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| ISSN: | 2169-3536 |