Observer based stabilization of discrete-time nonlinear systems

In this note we propose an observer based stabilization method for nonlinear discrete-time systems. The approach we use here is based on the stabilization method recently developed in [5] coupled with the EKO. From the Lyapunov approach, sufficient conditions for stability are deduced and expressed in terms of LMI that depend on arbitrary matrices fixed by the user. This has the advantage to enlarge the class of systems to be considered as it can be shown through numerical examples.