Fixed-Time Estimators of Derivatives of Unknown Maps

Abstract

A systematic and generalized asymptotic derivative estimator design method is first presented for unknown maps by adding a sinusoidal excitation signal to the argument of the map. Then, based on the proposed asymptotic derivative estimator approach and based on the existing design methods for both finite-time and fixed-time state observers, finite-time and fixed-time derivative estimators are designed. The sufficient conditions for finite-time and fixed-time input-to-state stable of the finite-time and fixed-time derivative estimators are given respectively when a bounded disturbance input exists.