On convergence of tracking differentiator

2011/04/01 by Bao-Zhu Guo, Bao‐Zhu Guo, Zhi-Liang Zhao +1 · 5 citations
Engineering · #Adaptive Control of Nonlinear Systems #Stability and Control of Uncertain Systems #Advanced Control Systems Optimization

paper · doi:10.1080/00207179.2011.569954

Abstract

The tracking differentiator was first proposed by Han in 1989 and the proof of convergence was presented the first time in Han and Wang (Han, J.Q., and Wang, W. (1994), ‘Nonlinear Tracking-differentiator’, Journal of Systems Science and Mathematical Science, 14, 177–183 (in Chinese)). Unfortunately, the proof there is incomplete. This problem has been open for over two decades. In this article, we give a rigorous proof under some additional conditions. An application for online estimation of the unknown frequencies for the finite sum of the sinusoidal signals is presented. The numerical simulations illustrate the effectiveness of the estimation for both linear and nonlinear tracking differentiators.

Citations

• Higher-order sliding modes, differentiation and output-feedback control

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