On convergence of extended state observers for nonlinear systems with non-differentiable uncertainties.

The analysis of convergence of extended state observers (ESOs) requires the total disturbance to be differentiable. However, this requirement is not satisfied in many control engineering practices. In this paper, we attempt to analyze the convergence of ESOs for nonlinear systems with non-differentiable uncertainties. A decomposition method is first presented to divide the non-differentiable total disturbance into a differentiable signal and a bounded but non-differentiable signal. Based on this decomposition, we give out the convergence of both nonlinear and linear ESOs (NLESO/LESO), low- and high-power ESOs (LPESO/HPESO), and fixed-time ESO (FxESO). We also derive the explicit formulas for the estimation errors of these ESOs. Simulations and experiments demonstrate the correctness of the analysis results. • The perturbation of ESO is established based on the proposed decomposition method. • The convergence of typical ESOs is analyzed when disturbance is non-differentiable. • Simulation and experimental testing of ESOs' convergence performance are carried out. [ABSTRACT FROM AUTHOR]