On the effect of perturbations on the stability of input-output linearizing controllers for a class of discrete-time nonlinear systems

An analysis of the effect of parameter perturbations on the stability of input-output linearizing controllers for a class of MIMO discrete-time nonlinear systems is presented. A static-state feedback is designed to input-output linearize a system without perturbations, and it is applied to the same system with an uncertain parameter vector, thus introducing an uncertain parameter term in the nominal input-output linearized system. It is shown that the state trajectories of the closed-loop perturbed system are ultimately bounded provided the closed-loop nominal system is exponentially stable and some conditions on the bounds of the perturbation terms are satisfied. (C) 1998 John Wiley & Sons, Ltd.