The nonlinear extended state observer (ESO) is a novel observer for a class of nonlinear control system. However, the non-smooth structure of the nonlinear ESO makes it difficult to measure the stability. In this paper, the stability problem of the nonlinear ESO is considered. The describing function (DF) method is adopted to analyze the stability of high-order nonlinear ESOs. The main result of the paper shows the existence of the self-oscillation and a sufficient stability condition for high-order nonlinear ESOs. Based on the analysis results, we give a simple and fast parameter tuning method for the nonlinear ESO and the active disturbance rejection control (ADRC). Realistic application simulations show the effectiveness of the proposed parameter tuning method.
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