An algorithm for linearization of discrete-time systems via restricted dynamic feedback

We extend the results in [H.G. Lee, et al., 1987] to multi-input systems, and utilize these to obtain necessary and sufficient conditions for the linearization of discrete-time nonlinear systems via restricted dynamic feedback. An algorithm to synthesize the dynamic feedback is also presented. We observe that for discrete-time nonlinear systems, the bound on the number of delays (or integrators) needed to synthesize the linearizing dynamic feedback differs from the continuous-time analogue.

[1]  M. Fliess,et al.  On Differentially Flat Nonlinear Systems , 1992 .

[2]  M. Fliess,et al.  Flatness and defect of non-linear systems: introductory theory and examples , 1995 .

[3]  Louis R. Hunt,et al.  Design for Multi-Input Nonlinear Systems , 1982 .

[4]  Nam Kwnaghee.  Linearization of discrete-time nonlinear systems and a canonical structure , 1989 .

[5]  A. Schaft.  Observability and Controllability for Smooth Nonlinear Systems , 1982 .

[6]  R. Su.  On the linear equivalents of nonlinear systems , 1982 .

[7]  D. M. Tilbury,et al.  A bound on the number of integrators needed to linearize a control system , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[8]  A. Arapostathis,et al.  Linearization of discrete-time systems , 1987 .

[9]  J. Lévine,et al.  On dynamic feedback linearization , 1989 .

[10]  Ari Arapostathis,et al.  Linearization of discrete-time systems via restricted dynamic feedback , 2003, IEEE Trans. Autom. Control..

[11]  W. Shadwick,et al.  Absolute equivalence and dynamic feedback linearization , 1990 .

[12]  Jessy W. Grizzle,et al.  Feedback Linearization of Discrete-Time Systems , 1986 .

[13]  Jean-Pierre Barbot,et al.  Discrete-time approximated linearization of SISO systems under output feedback , 1999, IEEE Trans. Autom. Control..

[14]  R. Gardner,et al.  The GS algorithm for exact linearization to Brunovsky normal form , 1992 .

[15]  D. W. Bacon,et al.  A condition for dynamic feedback linearization of control-affine nonlinear systems , 1997 .

[16]  Salvatore Monaco,et al.  Quadratic forms and approximate feed back linearization in discrete time , 1997 .

[17]  J. Lévine,et al.  Sufficient conditions for dynamic state feedback linearization , 1991 .

[18]  Hong-Tae Jeon,et al.  On the linearization via a restricted class of dynamic feedback , 2000, IEEE Trans. Autom. Control..

[19]  Pierre Rouchon.  Necessary Condition and Genericity of Dynamic Feedback Linearization , 1994 .

[20]  B. Jakubczyk,et al.  Remarks on Equivalence and Linearization of Nonlinear Systems , 1992 .

[21]  C. Moog,et al.  A linear algebraic framework for dynamic feedback linearization , 1995, IEEE Trans. Autom. Control..

[22]  W. Sluis.  A necessary condition for dynamic feedback linearization , 1993 .