The immersion under feedback of a multidimensional discrete-time non-linear system into a linear system

Abstract

This paper deals with the problem of finding conditions which ensure the reproducibility of the input-output behaviour of a linear analytic discrete-time system by means of a linear discrete-time system. On this basis the problem of modifying the system by feedback in order for it to enjoy such a property is posed and solved.

A constructive condition for dynamic feedback linearization

“…The ÿrst works deal with the exact linearization problem [4,5,10,12,[14][15][16][17][18], while dynamic solutions were considered in [6,13,19]. In [7], su cient geometric conditions via prolongations and di eomorphism were given.…”

Dynamic Feedback Linearization of Two Input Nonlinear Systems

“…The static state feedback linearization problem has been widely studied both in continuous and discrete time (see Brockett [1978], Jakubczyk et al [1980], Isidori et al [1981], Hunt et al [1983], Marino [1986], Monaco et al [1986], Jakubczyk [1987], Lee et al [1987], Isidori [1989], Nijmeijer et al [1990], Califano et al [1999]). Dynamic solutions were first considered in Isidori et al [1986], Monaco et al [1987] and Charlet et al [1989]. In Charlet et al [1991], sufficient conditions were given for the solvability of the problem via prolongations and diffeomorphism.…”

Algebraic necessary and sufficient conditions of input-output linearization

“…Most of the works on this subject have considered the solution of this problem by static-state feedback (see [6,45,29,30,44,27,3,4,2,34,23,7] for continuous time and [39,38,36] for discrete time). Most of the works on this subject have considered the solution of this problem by static-state feedback (see [6,45,29,30,44,27,3,4,2,34,23,7] for continuous time and [39,38,36] for discrete time).…”