Discussion on: A Comparison of Sliding Mode and Unknown Input Observer for Fault Reconstruction

where x(t) ∈ IR is the state, u(t) ∈ IR is the known input, v(t) ∈ IR is the unknown input, which can be considered as the effect of the actuator failure, and y(t) ∈ IR is the measurement output. Without loss of generality, we have rank D = q and rankC = p. The problem of the state estimation in this case is the well known unknown input one, see [4] and the references given in [2]. The necessary and sufficient conditions for the existence and the stability of the full order or reduced order observers are