Parameterized Feedback Linearization of Nonlinear Discrete-Time Control Systems

The paper studies the possibility to feedback linearize the state equations of a nonlinear reversible single-input discrete-time control system by a parametrized state transformation and a static state feedback. The transformations used in this paper differ from the standard ones by allowing them to depend also on a certain number of the past values of the input variable, which are considered as known parameters. Thus, the problem generalizes the standard static state feedback linearization problem. It is shown that whenever one is able to find a fictitious output function from which all states are observable, then there exist the parametrized transformations, which linearize system dynamics. This result enlarges significantly the class of nonlinear systems which can be feedback linearized. The proposed approach is illustrated by a thrust controlled vehicle example.