Observer design for a class of nonlinear systems with non-full relative degree

The paper proposes a method for observer design for a class of nonlinear systems. We decompose the system using a weaker concept than the relative degree. We provide sufficient conditions for global asymptotic stability of the error dynamics. The observer design is carried out by means of a change of coordinates combined with a high gain technique. In particular, our approach results in an observer gain vector field which is extraordinary easy to compute.

[1]  R. Penrose.  A Generalized inverse for matrices , 1955 .

[2]  C. Desoer,et al.  Global inverse function theorem , 1972 .

[3]  Adi Ben-Israel,et al.  Generalized inverses: theory and applications , 1974 .

[4]  C. D. Meyer,et al.  Generalized inverses of linear transformations , 1979 .

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

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

[7]  W. Boothby.  Some comments on global linearization of nonlinear systems , 1984 .

[8]  A. Isidori.  Nonlinear Control Systems: An Introduction , 1986 .

[9]  W. Respondek.  Global Aspects of Linearization, Equivalence to Polynomial Forms and Decomposition of Nonlinear Control Systems , 1986 .

[10]  G. Burstein.  Algebraic and geometric methods in nonlinear control theory , 1988 .

[11]  A. Isidori,et al.  New results and examples in nonlinear feedback stabilization , 1989 .

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

[13]  Bram de Jager.  Symbolic calculation of zero dynamics for nonlinear control systems , 1991, ISSAC '91.

[14]  A. Isidori,et al.  Asymptotic stabilization of minimum phase nonlinear systems , 1991 .

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

[16]  A. Germani,et al.  A Luenberger-like observer for nonlinear systems , 1993 .

[17]  Alfredo Germani,et al.  A state observer for nonlinear dynamical systems , 1997 .

[18]  Eduardo Sontag,et al.  Output-to-state stability and detectability of nonlinear systems , 1997 .

[19]  R. Rajamani.  Observers for Lipschitz nonlinear systems , 1998, IEEE Trans. Autom. Control..

[20]  G. L. Amicucci,et al.  On nonlinear detectability , 1998 .

[21]  H. Hammouri,et al.  Observer design for a special class of nonlinear systems , 1998 .

[22]  Nam Hoon Jo,et al.  Input output linearization approach to state observer design for nonlinear system , 2000, IEEE Trans. Autom. Control..

[23]  Jin H. Seo,et al.  A state observer for nonlinear systems and its application to ball and beam system , 2000, IEEE Trans. Autom. Control..

[24]  Jin H. Seo,et al.  Observer design for non-linear systems that are not uniformly observable , 2002 .

[25]  Manfredi Maggiore,et al.  A Separation Principle for Non-UCO Systems , 2002 .

[26]  Mohammed M'Saad,et al.  Observer design for a class of MIMO nonlinear systems , 2004, Autom..

[27]  Klaus Röbenack,et al.  Zum High-Gain-Beobachterentwurf für eingangs-/ausgangslinearisierbare SISO-Systeme (About High Gain Observer Design for Input-Output Linearizable SISO Systems) , 2004 .