On convergence of extended state observers for discrete-time nonlinear systems

The extended state observer, a crucial part of the active disturbance rejection control, was first proposed in 1995 by Jingqing Han. The discrete-time form of the extended state observer has been extensively used in many practical applications in engineering such as quad-rotor robot control and non-circular machining control; the convergence property of the discrete-time n-dimensional extended state observer, however, remains unexplored and is investigated in this work. The main idea is to construct the error equations of the discrete-time extended state observer for an n-dimensional single-input-single-output nonlinear system with uncertainty, and to prove the convergence of the extended state observer through induction.