ON DYNAMIC INPUT-OUTPUT LINEARIZATION OF DISCRETE-TIME NONLINEAR-SYSTEMS

This paper studies the problem of linearizing the input-output map of an analytic discrete-time nonlinear system locally around a given traj ectory. Necessary and sufficient conditions are given for the existenc e of a regular dynamic state feedback control law under which the inpu t-dependent part of the response of a nonlinear system becomes linear in the input and independent of the initial state. The proposed condit ions are less restrictive than those obtained by Lee and Marcus for li nearizing the input-output map via a static-state feedback. Instrument al in the problem solution is the inversion (structure) algorithm for a discrete-time nonlinear system. Firstly, the solvability conditions are expressed in terms of the inversion algorithm. Secondly, the proof of the existence and construction of the dynamic state feedback compe nsator relies on this algorithm.