On the Linearization Up to Multi-Output Injection for a Class of Systems With Implicitly Defined Outputs

For a class of nonlinear systems, we investigate the problem of under what conditions there exists a coordinate transformation that yields a state affine linear system up to output injection with implicit outputs. In particular, we provide necessary and sufficient conditions for time-varying linearization up to multi-output injection. We highlight that if the conditions hold, as a consequence, it is possible in the new coordinates to construct an observer with linear error dynamics. We propose a methodology to find the coordinate transformation. Several examples illustrate the proposed procedure.

[1]  J. Gauthier,et al.  Bilinearization up to output injection , 1988 .

[2]  V. Jurdjevic.  Geometric control theory , 1996 .

[3]  Antonio Pedro Aguiar,et al.  ON THE LINEARIZATION UP TO MULTI-OUTPUT INJECTION FOR A CLASS OF NONLINEAR SYSTEMS WITH IMPLICITLY DEFINED OUTPUTS , 2012 .

[4]  Hassan Hammouri,et al.  A new procedure for time-varying linearization up to output injection , 1996 .

[5]  João Pedro Hespanha,et al.  Robust filtering for deterministic systems with implicit outputs , 2009, Syst. Control. Lett..

[6]  Antonio Pedro Aguiar,et al.  A new algorithm for linearization up to multi-output and multi-input injection for a class of systems with implicitly defined outputs , 2013, 2013 European Control Conference (ECC).

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

[8]  Philippe Martin,et al.  A Lie-Backlund approach to equivalence and flatness of nonlinear systems , 1999, IEEE Trans. Autom. Control..

[9]  João Pedro Hespanha,et al.  Minimum-energy state estimation for systems with perspective outputs , 2006, IEEE Transactions on Automatic Control.

[10]  Driss Boutat,et al.  On the transformation of nonlinear dynamical systems into the extended nonlinear observable canonical form , 2011, Int. J. Control.

[11]  J. Gauthier,et al.  Global time-varying linearization up to output injection , 1992 .

[12]  G. Besançon.  An Overview on Observer Tools for Nonlinear Systems , 2007 .

[13]  Franck Plestan,et al.  Linearization by completely generalized input-output injection , 1999, Kybernetika.

[14]  H. Hammouri,et al.  The time-varying linearization up to output injection , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[15]  Hassan Hammouri,et al.  High Gain Observer for Structured Multi-Output Nonlinear Systems , 2010, IEEE Transactions on Automatic Control.

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

[17]  C. Moog,et al.  New algebraic-geometric conditions for the linearization by input-output injection , 1996, IEEE Trans. Autom. Control..

[18]  Driss Boutat,et al.  Extended nonlinear observable canonical form for multi-output dynamical systems , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[19]  M. D. Carmo.  Differential forms and applications , 1994 .

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

[21]  O. Grasselli,et al.  An existence theorem for observers of bilinear systems , 1981 .

[22]  A. Krener.  On the Equivalence of Control Systems and the Linearization of Nonlinear Systems , 1973 .

[23]  A. Agrachev,et al.  Control Theory from the Geometric Viewpoint , 2004 .