Performance Assessment of Discrete-Time Extended State Observers: Theoretical and Experimental Results

This paper evaluates the performance of the discrete-time linear extended state observer (ESO) for a disturbed nonlinear discrete-time system with uncertainties. Since the performance of the ESO is dominated by the choice of the gain parameter, the goal of this paper is to analyze the behavior of the observation error when the gain parameter varies from zero to infinity. We show that for the ESO considered, there exists a certain threshold such that if the gain parameter is smaller than this threshold, the observation error at steady state will become unbounded. An upper bound on the asymptotic observation error is also proposed, which is proved to be bounded and convergent utilizing set-theoretic techniques. For the case where the closed-loop matrix of the ESO is nonnegative, a tighter upper bound on the asymptotic observation error is also proposed. The proposed theoretic results are illustrated by the simulation results and the experimental verifications on a direct current motor loading platform.