Controller and observer normal forms in discrete-time

Up to what extent is it possible to simplify the nonlinearities of a given discrete-time system through transformations involving feedbacks or outputinjections? Solutions to these problems, at the basis of several control and state estimation design procedures, take advantage of a combined use of geometric and algebraic methods, two major setups in nonlinear control theory strongly influenced by the fundamental work of Alberto Isidori. Links between these frameworks are illustrated in the present paper which is written to celebrate his 65th birthday. © 2008 Springer-Verlag