Nonlinear continuous integral-derivative observer

In this paper, a high-order nonlinear continuous integral-derivative observer is presented based on finite-time stability and singular perturbation technique. The proposed integral-derivative observer can not only obtain the multiple integrals of a signal, but can also estimate the derivatives. Conditions are given ensuring finite-time stability for the presented integral-derivative observer, and the stability and robustness in time domain are analysed. The merits of the presented integral-derivative observer include its synchronous estimation of integrals and derivatives, finite-time stability, ease of parameters selection, sufficient stochastic noises rejection and almost no drift phenomenon. The theoretical results are confirmed by computational analysis and simulations.