Arbitrary-Order Fixed-Time Differentiators

Differentiation is an important task in control, observation, and fault detection. Levant’s differentiator unique, since it able to estimate exactly robustly the derivatives of a signal with bounded high-order derivative. However, convergence time, although finite, grows unboundedly norm initial differentiation error, making uncertain when estimated derivative exact. In this article, we propose extension so that worst-case time can be arbitrarily assigned independently condition, i.e., estimation converges fixed time . We also family continuous differentiators provide unified Lyapunov framework for analysis design.