Sliding mode state observers for discrete-time linear systems

In discrete-time systems, instead of having a hyperplane as in the continuous case, there is a countable set of points comprising a so-called lattice; and the surface on which these sliding points lie is named the latticewise hyperplane. In this paper an asymptotically stable observer for discrete-time systems is designed by using the properties of the sliding mode such that the stability of the error system in the sliding mode is maintained. Various techniques for finding the feedforward injection map are proposed. The stability of the reconstruction error system with a bounded perturbation signal is studied.