An Exact Robust High-Order Differentiator With Hyperexponential Convergence

• 成果类型: Article
• 署名作者: Wang, Jian; Zimenko, Konstantin; Polyakov, Andrey; Efimov, Denis
• 署名单位: Hangzhou Dianzi University; ITMO University; Universite de Lille; Inria; Centrale Lille; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Information Sciences & Technologies (INS2I)
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3435954
• 发表日期: 2025
• 页码: 627-634
• 关键词: Observers; CONVERGENCE; Noise measurement; noise; vectors; Perturbation methods; Measurement uncertainty; Convergence of numerical methods; observers; State estimation

摘要

A linear time-varying state observer is presented for a chain of integrators having bounded disturbances in the last equation. It is demonstrated that in the noise-free setting, for the continuous-time realization, the estimation error converges to zero with a hyperexponential rate (faster than any exponential) uniformly in the disturbance. An implicit discretization scheme of the observer is proposed, which in the discrete time preserves all the main properties of the continuous-time counterpart. In addition, the discrete-time estimation error is robustly stable with respect to the measurement noise. The efficiency of the suggested observer is illustrated through comparison with a linear high-gain observer and a sliding-mode high-order differentiator.