Nonlinear discrete-time state feedback regulators with assignable closed-loop dynamics

This paper proposes a new approach to the nonlinear discrete-time state feedback regulator synthesis problem with assignable closed-lop dynamics. The problem´s formulation is realized through a system of nonlinear functional equations and a rather general set of necessary and sufficient conditions for solvability is derived. Using tools from functional equations theory, one can prove that the solution to the above system of nonlinear functional equations is locally analytic, and an easily programmable series solution method can be developed. Under a simultaneous implementation of a nonlinear coordinate transformation and a nonlinear discrete-time state feedback control law that are both computed through the solution of the system of nonlinear functional equations, the feedback linearization with pole-placement design objective can be attained under rather general conditions