A note on versions:The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Abstract: A nonlinear integral-uncertainty observer is presented, which can estimate the integral of measurement output signal and the uncertainty in system, synchronously. In order to be satisfied with the existing hardware computational environments and to select the parameters more easily, a simplified linear version of the nonlinear integral-uncertainty observer is also developed. The effectiveness of the proposed observers are verified through the numerical simulations and experiments: i) through the integral-uncertainty observers, the attitude angle and the uncertainties in attitude dynamics are estimated synchronously from the measurements of angular velocity, and the estimate results by the two observers are compared; ii) a control law is designed based on the observers to drive the jet aircraft to track a reference trajectory.