Quadratic dynamic feedback linearization with observer in discrete time

The design of nonlinear discrete-time control schemes is quite difficult to handle. This is in part due to the nonlinear action of the control generated by the composition of functions. It results that input-state and input-output behaviours are not easily characterised and that the conditions for feedback linearization under static feedback are quite restrictive as an example. In order to relax some of these conditions in the continuous-time case, discrete-time feedback linearization in an approximated meaning can be studied. A first step in this direction is to consider quadratic approximations. The interest of such approximation at the degree two was previously shown by the authors (1993); any linearly controllable nonlinear discrete-time dynamics can be linearized up to an error of order three thanks to a dynamic state feedback. In order to enlarge the applicability of the control scheme it is completed with P observer scheme