Exponential Observers for Discrete-Time Nonlinear Systems with Incremental Quadratic Constraints

This paper investigates the observer design for a class of nonlinear discrete-time systems satisfying incremental quadratic constraints. A circle criterion based full-order observer is constructed by injecting output estimation error into the observer nonlinear terms. We also construct a reduced-order observer to estimate the unmeasured system state. The proposed observers guarantee exponential convergence of the estimation error to zero. The design of the proposed observers is reduced to solving a set of linear matrix inequalities. It is proved that the conditions under which a full-order observer exists also guarantee the existence of a reduced-order observer. Compared to some previous results in the literature, this work considers a larger class of nonlinearities and unifies some related observer designs for discrete-time nonlinear systems. Finally, a numerical example is given to illustrate the effectiveness of the proposed design.