  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.
