An extended unknown input observer for nonlinear discrete-time systems

This paper is focused on the problem of designing nonlinear observers for fault diagnosis tasks. The main objective is to show how to employ a modified version of the well-known unknown input observer, which can be applied to linear stochastic systems, to form a nonlinear deterministic observer. Moreover, it is shown that the convergence of the proposed observer is ensured under certain conditions. In particular an unknown diagonal matrix is introduced to take the linearization errors into account, and then the Lyapunov method is employed to obtain convergence conditions. Moreover, a simple technique to increasing the convergence rate is presented as well. The final part of this paper shows an example, concerning state estimation of an induction motor, which confirms the effectiveness of the approach.