Observer Design for Lipschitz Nonlinear Systems: The Discrete-Time Case

This brief deals with observer design for a class of discrete-time nonlinear systems, namely, linear systems with Lipschitz nonlinearities. Perhaps one of the main features, with respect to the existing results, is the use of new particular Lyapunov functions to deduce nonconservative conditions for asymptotic convergence of the state estimation errors. The established sufficient conditions are expressed in terms of linear matrix inequalities, which are easily and numerically tractable by standard software algorithms. By means of simple transformations, a reduced-order version is established where the observer gain is computed in an optimal manner. Performances of the proposed approach are illustrated through simulation and experimental results; one of them concerns synchronization of chaotic nonlinear models

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

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

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

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

[5]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[6]  J. Gauthier,et al.  Erratum Observability and Observers for Nonlinear Systems , 1995 .

[7]  R. Rajamani,et al.  A systematic approach to adaptive observer synthesis for nonlinear systems , 1995, Proceedings of Tenth International Symposium on Intelligent Control.

[8]  Alberto Tesi,et al.  Dead-beat chaos synchronization in discrete-time systems , 1995 .

[9]  J. Suykens,et al.  Robust nonlinear H/sub /spl infin// synchronization of chaotic Lur'e systems , 1997 .

[10]  Johan A. K. Suykens,et al.  Robust Nonlinear H Synchronization of Chaotic Lur'e Systems , 1997 .

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

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

[13]  Konrad Reif,et al.  The extended Kalman filter as an exponential observer for nonlinear systems , 1999, IEEE Trans. Signal Process..

[14]  Teh-Lu Liao,et al.  An observer-based approach for chaotic synchronization with applications to secure communications , 1999 .

[15]  Mohamed Boutayeb,et al.  A strong tracking extended Kalman observer for nonlinear discrete-time systems , 1999, IEEE Trans. Autom. Control..

[16]  Konrad Reif,et al.  Nonlinear state observation using H∞-filtering Riccati design , 1999, IEEE Trans. Autom. Control..

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

[18]  Zhengzhi Han,et al.  A note on observers for Lipschitz nonlinear systems , 2002, IEEE Trans. Autom. Control..

[19]  M. Boutayeb,et al.  Generalized state-space observers for chaotic synchronization and secure communication , 2002 .

[20]  G. Grassi,et al.  Theory and experimental realization of observer-based discrete-time hyperchaos synchronization , 2002 .

[21]  Mohamed Boutayeb,et al.  Synchronization and input recovery in digital nonlinear systems , 2004, IEEE Transactions on Circuits and Systems II: Express Briefs.

[22]  P. Pagilla,et al.  Controller and observer design for Lipschitz nonlinear systems , 2004, Proceedings of the 2004 American Control Conference.

[23]  A. Alessandri Design of observers for lipschitz nonlinear systems using LMI , 2004 .

[24]  Ali Zemouche,et al.  Observer synthesis for Lipschitz discrete-time systems , 2005, 2005 IEEE International Symposium on Circuits and Systems.