LINEARIZATION OF DISCRETE-TIME-SYSTEMS

The algebraic formalism developed in this paper unifies the study of t he accessibility problem and various notions of feedback linearizabili ty for discrete-time nonlinear systems. The accessibility problem for nonlinear discrete-time systems is shown to be easy to tackle by means of standard linear algebraic tools, whereas this is not the case for nonlinear continuous-time systems, in which case the most suitable app roach is provided by differential geometry. The feedback linearization problem for discrete-time systems is recasted through the language of differential forms. In the event that a system is not feedback linear izable, the largest feedback linearizable subsystem is characterized w ithin the same formalism using the notion of derived flag of a Pfaffia n system. A discrete-time system may be linearizable by dynamic state feedback, though it is not linearizable by static state feedback. Nece ssary and sufficient conditions are given for the existence of a so-ca lled linearizing output, which in turn is a sufficient condition for d ynamic state feedback linearizability.