Exact State Reconstruction for LTI-Systems with Non-Differentiable Unknown Inputs

In this paper, a sliding mode based observer design for strongly observable systems in the presence of non-differentiable unknown inputs is presented. The system state is reconstructed in finite time by means of a linear observer in combination with a robust exact differentiator. By appropriate filtering of the measured output, differentiation of signal components involving the unknown input is avoided. For strongly detectable systems, the proposed technique is combined with invariant subspace methods to provide asymptotic reconstruction of the state. A numerical simulation example demonstrates the performance of the proposed approach.