Verifiable Conditions for Multioutput Observer Error Linearizability

The verifiable necessary and sufficient conditions for the multioutput observer error linearization problem have not been found over the last three decades. In this technical note, we give the unverifiable necessary and sufficient conditions which are more specific than the ones in the literature. Using these conditions, a verifiable sufficient condition (also necessary with additional restriction on the problem) is derived. Since our proofs are constructive, a desired state transformation can also be found in the theorem. Also our algorithmic conditions can be easily implemented by a MATLAB programming.

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

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

[3]  Juhoon Back,et al.  Dynamic Observer Error Linearization , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

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

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

[6]  Anthony M. Bloch,et al.  Nonlinear Dynamical Control Systems (H. Nijmeijer and A. J. van der Schaft) , 1991, SIAM Review.

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

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

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

[10]  A. Isidori.  Nonlinear Control Systems , 1985 .

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

[12]  Claude H. Moog,et al.  The Observer Error Linearization Problem via Dynamic Compensation , 2014, IEEE Transactions on Automatic Control.

[13]  D. Luenberger.  Canonical forms for linear multivariable systems , 1967, IEEE Transactions on Automatic Control.

[14]  Alberto Isidori,et al.  Nonlinear control systems: an introduction (2nd ed.) , 1989 .

[15]  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.

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

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

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

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

[20]  Riccardo Marino,et al.  Nonlinear control design , 1995 .

[21]  Hong-Tae Jeon,et al.  Restricted dynamic observer error linearizability , 2015, Autom..