A new reduced-order observer normal form for nonlinear discrete time systems

This paper presents a new observability normal form for discrete-time nonlinear systems. This form enables us to design a reduced-order observer. Necessary and sufficient geometrical conditions for the existence of a coordinate change to transform a discrete-time nonlinear system into such normal form are given. An illustrative example is given to show the effectiveness of our approach.

[1]  X. Xia,et al.  Non-linear observer design by observer canonical forms , 1988 .

[2]  Driss Boutat,et al.  Observability analysis by Poincaré normal forms , 2009, Math. Control. Signals Syst..

[3]  M. Darouach,et al.  A canonical discrete-time nonlinear form for reduced order observers design , 2011 .

[4]  D. Luenberger.  Observing the State of a Linear System , 1964, IEEE Transactions on Military Electronics.

[5]  Driss Boutat,et al.  New algorithm for observer error linearization with a diffeomorphism on the outputs , 2009, Autom..

[6]  A. Phelps.  On constructing nonlinear observers , 1991 .

[7]  W. Rugh.  Linear System Theory , 1992 .

[8]  Arthur J. Krener,et al.  Linearization by output injection and nonlinear observers , 1983 .

[9]  MingQing Xiao,et al.  A direct method for the construction of nonlinear discrete-time observer with linearizable error dynamics , 2006, IEEE Transactions on Automatic Control.

[10]  Tzyh Jong Tarn,et al.  Exponential Observers for Nonlinear Dynamic Systems , 1975, Inf. Control..

[11]  A. Krener,et al.  Nonlinear observers with linearizable error dynamics , 1985 .

[12]  F. Thau.  Observing the state of non-linear dynamic systems† , 1973 .

[13]  Driss Boutat,et al.  A nonlinear canonical form for reduced order observer design , 2010 .

[14]  C. Kravaris,et al.  Nonlinear observer design using Lyapunov's auxiliary theorem , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[15]  Kwanghee Nam,et al.  Observer design for nonlinear discrete-time systems , 1990, 29th IEEE Conference on Decision and Control.

[16]  V. Sundarapandian,et al.  Reduced order observer design for discrete-time nonlinear systems , 2006, Appl. Math. Lett..

[17]  D. Boutat,et al.  Quadratic observability normal form , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[18]  Mohamed Darouach.  Existence and design of functional observers for linear systems , 2000, IEEE Trans. Autom. Control..

[19]  M. Boutayeb,et al.  A reduced-order observer for non-linear discrete-time systems , 2000 .

[20]  V. Sundarapandian,et al.  New results on general observers for discrete-time nonlinear systems , 2004, Appl. Math. Lett..

[21]  Driss Boutat,et al.  Geometrical conditions for observer error linearization with a diffeomorphism on the outputs , 2007 .

[22]  J. Gauthier,et al.  A simple observer for nonlinear systems applications to bioreactors , 1992 .

[23]  MingQing Xiao,et al.  Nonlinear Observer Design in the Siegel Domain , 2002, SIAM J. Control. Optim..