Stability robustness of linearizing controllers with state estimation for discrete-time nonlinear systems

We discuss the effect of parameter uncertainty on the stability of the closed-loop system regulated by a state feedback that linearizes a nominal discrete-time nonlinear system which includes an observer. We show that the stability of the perturbed closed-loop system is assured if the closed-loop nominal system has an exponentially stable equilibrium point including an exponential observer, and provided some other conditions on the perturbation magnitude are also satisfied. An analysis of the effect of parameter perturbations on the stability of input-state linearizing controllers that make use of a state estimator, is presented.