Abstract
Conventional sliding-modes based differentiators make it possible to estimate successive derivatives of a given time-varying signal in finite-time and with exact convergence in noise free case. In general, the convergence time is an unbounded increasing function of initial estimation errors. Most already proposed solutions guarantee a convergence in a maximum time independent of initial conditions. In this paper, novel sliding mode differentiators with a prescribed convergence time are proposed. The convergence time can be chosen arbitrary whatever large initial estimation errors. The proposed key solution is based on a time-dependent transformation using modulating functions which make it possible to cancel the effect of initial conditions on the convergence time. New arbitrary order differentiators including the super-twisting algorithm based on modulating functions are introduced. Lyapunov functions and homogeneity tools are used to prove the convergence of the proposed first-order and arbitrary order differentiators, respectively. Robustness with respect to measurement noise is also addressed.
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