Sliding-mode observers for uncertain systems

Sliding-mode observer design is considered for linear systems with unknown inputs when the so-called observer matching condition is not satisfied. To circumvent the restriction imposed by the observer matching condition, the method of utilizing auxiliary outputs generated by high-order sliding-mode exact differentiators in the sliding-mode observer design has been proposed in the literature. In this paper, an alternative approach is proposed to use high-gain approximate differentiators of simpler architecture instead of high-order sliding-mode exact differentiators. The capability of reconstructing the unknown inputs using the proposed high-gain approximate differentiator based sliding-mode observer is also discussed and then illustrated with a numerical example.