A novel unknown input interval observer for systems not satisfying relative degree condition

In this article, a novel unknown input interval observer (UIIO) is proposed for systems not satisfying the relative degree condition. In interval estimation, estimation errors are required not only positive but also convergent. For this purpose, some works combined unknown input observer with interval estimation, namely UIIO where by virtue of some transformations, some states are expressed as functions of outputs and other states which are decoupled from the unknown input. Nevertheless, complete decoupling can be guaranteed when the systems satisfy relative degree condition, which does not hold for some practical systems. Although some works have been done to relax the requirement on relative degree condition, they usually construct auxiliary outputs using high-order differentiators which necessitates that the signals are smooth enough as well as that their derivatives are bounded, limiting the application of existing approaches and also increasing the computational cost. Motivated by the discussions above, a novel UIIO scheme combining the interval observation technique with adaptive sliding mode is proposed, without the relative degree condition and free from differentiating signals, hence the design process is simplified and the computational cost is decreased. Finally, simulations are conducted to verify the effectiveness of the proposed scheme.