Observer for discrete-time Lipschitz non-linear systems with delayed output

This study presents an observer design method for discrete-time non-linear systems which have Lipschitz non-linearity and delayed output. The proposed observer has a chained form that allows us to estimate a system state sequentially from delayed output measurement. Based on an observer design for discrete-time systems without output delay, it is shown that the proposed observer guarantees the exponential convergence to zero of the estimation error in spite of the presence of output measurement delay. Finally, a numerical example is given to verify the effectiveness of our design approach.