• adaptive update law;
  • velocity estimator;
  • acceleration estimator;
  • LMI


The design of an ideal differentiator is a difficult and a challenging task. In this paper, we propose two types of differentiators to estimate the time derivative of an output signal. To begin with, a velocity estimator is proposed on the basis of the adaptive identification method and compared with the exact differentiator proposed by Levant. Then, an acceleration estimator is proposed with the nonpassifiable adaptive schemes. Finally, the proposed differentiators are applied to the estimation of the speed and acceleration of the mass–spring system. The simulation results show that the proposed differentiators are robust to additive noises. Copyright © 2010 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.