Stability analysis of linearizing controllers for a class of perturbed nonlinear discrete-time systems

A robustness analysis of a linearizing controller for nonlinear discrete-time systems is presented. The controller is designed for a fully linearizable nominal system, but it is applied to a system perturbed by a changing parameter vector. It is shown that if the closed-loop nominal system is asymptotically stable then the closed-loop perturbed system is also stable if some conditions on a perturbed term are satisfied. The results are applied to the chaotic Henon system regulated by a linearizing controller.