Discrete-Time Observer Error Linearizability via Restricted Dynamic Systems

In this technical note, we define the observer error linearization problem of a discrete-time autonomous nonlinear system via a restricted dynamic system. This is the dual to restricted dynamic feedback linearization in a loose sense. Necessary and sufficient conditions for this problem are obtained in terms of the index.

[1]  J. Grizzle,et al.  The Extended Kalman Filter as a Local Asymptotic Observer for Nonlinear Discrete-Time Systems , 1992, 1992 American Control Conference.

[2]  Hong-Gi Lee,et al.  Algebraic conditions for state equivalence to a discrete-time nonlinear observer canonical form , 2011, Syst. Control. Lett..

[3]  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.

[4]  Kwanghee Nam,et al.  Observer design for autonomous discrete-time nonlinear systems , 1991 .

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

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

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

[8]  D. Bestle,et al.  Canonical form observer design for non-linear time-variable systems , 1983 .

[9]  Wei Lin,et al.  Remarks on linearization of discrete-time autonomous systems and nonlinear observer design , 1995 .

[10]  H. J. C. Huijberts,et al.  On existence of extended observers for nonlinear discrete-time systems , 1999 .

[11]  Costas Kravaris,et al.  Discrete-time nonlinear observer design using functional equations , 2001 .

[12]  MingQing Xiao,et al.  Erratum: Nonlinear Observer Design in the Siegel Domain , 2004, SIAM J. Control. Optim..

[13]  V. Sundarapandian,et al.  Observer design for discrete-time nonlinear systems , 2002 .

[14]  Jin H. Seo,et al.  Nonlinear observer design by dynamic observer error linearization , 2004, IEEE Transactions on Automatic Control.

[15]  Nahum Shimkin,et al.  Nonlinear Control Systems , 2008 .

[16]  J. Lévine,et al.  Nonlinear system immersion, observers and finite-dimensional filters , 1986 .

[17]  M. Hou,et al.  Observer with linear error dynamics for nonlinear multi-output systems , 1999 .

[18]  Alfredo Germani,et al.  A robust observer for discrete time nonlinear systems , 1995 .

[19]  H. Keller Non-linear observer design by transformation into a generalized observer canonical form , 1987 .

[20]  Costas Kravaris,et al.  Nonlinear discrete-time observer design with linearizable error dynamics , 2003, IEEE Trans. Autom. Control..

[21]  Guillaume J.J. Ducard,et al.  Nonlinear Control Design , 2009 .

[22]  Gildas Besançon,et al.  On output transformations for state linearization up to output injection , 1999, IEEE Trans. Autom. Control..

[23]  J. Grizzle,et al.  Observer design for nonlinear systems with discrete-time measurements , 1995, IEEE Trans. Autom. Control..

[24]  Dorothée Normand-Cyrot,et al.  On the observer design in discrete-time , 2003, Syst. Control. Lett..

[25]  X. Xia,et al.  Nonlinear observer design by observer error linearization , 1989 .

[26]  Salvatore Monaco,et al.  Canonical observer forms for multi-output systems up to coordinate and output transformations in discrete time , 2009, Autom..

[27]  J. W. GRIZZLEt Sampled-data Observer Error Linearization , 2022 .

[28]  Ari Arapostathis,et al.  Necessary and Sufficient Conditions for State Equivalence to a Nonlinear Discrete-Time Observer Canonical Form , 2008, IEEE Transactions on Automatic Control.

[29]  Arjan van der Schaft,et al.  Non-linear dynamical control systems , 1990 .

[30]  Philippe Jouan Immersion of Nonlinear Systems into Linear Systems Modulo Output Injection , 2003, SIAM J. Control. Optim..

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