Dynamic output linearization of nonlinear discrete-time control systems

The problem of dynamic output feedback equivalence of nonlinear observable discrete-time control systems with outputs has been studied by Pawluszewics-Bartosiewics. In this paper we use those results to achieve equivalence of a nonlinear system to a linear one. In this way we obtain an algebraic criterion of dynamic output linearization for discrete-time systems. We recall the concept of anticipating output equivalence, where transformations of outputs and controls depend on future values, and the concept of dynamic output equivalence, depending on past and present controls and outputs values. In order to give the criterion of linearisation of a discrete-time control system we have to use the difference output algebra and the difference output universe associated with the given system.