Nonlinear observer design with an appropriate Riemannian metric

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2009, Pages 6514-6519

  Sanfelice, Ricardo G ^a   Praly, Laurent ^b  

^a University of Arizona   (United States)

^b PSL RESEARCH UNIVERSITY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

GEODESY; ORDINARY DIFFERENTIAL EQUATIONS; TENSORS;

ESTIMATED STATE; ESTIMATION ERRORS; GEODESIC CONVEXITIES; GEODESIC DISTANCES; LOCAL OBSERVABILITY; NONLINEAR OBSERVER DESIGN; OUTPUT FUNCTIONS; RIEMANNIAN METRICS;

GEOMETRY;

EID: 77950890998     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2009.5400714     Document Type: Conference Paper

References (19)

1. N. Aghannan and P. Rouchon. An intrinsic observer for a class of lagrangian systems. IEEE Trans. Automatic Control, 48(6):936-945, 2003.
2. M. Arcak and P. Kokotović. Observer based control of systems with slope-restricted nonlinearities. IEEE Trans. Automatic Control, 46(7):1146-1150, 2001.
3. S. Bonnabel. Observateurs Asymptotiques Invariants. PhD thesis, Spécialité Mathématiques et Automatique. É cole des Mines de Paris, 2007.
4. W. M. Boothby. An Introduction to Differentiable Manifolds and Riemannian Geometry. Academic Press, 1975.
5. B. P. Demidovich. Dissipativity of a nonlinear system of differential equations. Ser. Mat; Mekh. Part I.6 (1961);
6. B. P. Demidovich. Dissipativity of a nonlinear system of differential equations. Ser. Mat; Mekh. Part II.1, 3-8(1962) (in Russian)., pages 19-27.
7. M.P. DoCarmo. Riemannian Geometry. Birkhauser, Boston, 1992.
8. P. Hartmann. Ordinary differential equations. Wiley, 1964.
9. N. J. Hicks. Notes on Differential Geometry. Van Nostrand Publishing Company, Princeton, New Jersey, 1965.
10. G. Isac and S. Z. Németh. Scalar and asymptotic scalar derivatives : theory and applications. Springer, 4th edition, 2008.
11. J. Jouffroy. Some ancestors of contraction analysis. Proc. IEEE Conference on Decision and Control, pages 5450-5455, 2005.
12. L. P. Lebedev and M. J. Cloud. Tensor analysis. Norwood Mass., 2005.
13. D. C. Lewis. Metric properties of differential equations. American Journal of Mathematics, 71:294-312, 1949.
14. W. Lohmiller and J.-J. Slotine. On contraction analysis for nonlinear systems. Automatica, 34(6):671-682, 1998.
15. S. Z. Németh. Geometric aspects of Minty-Browder monotonicity. PhD thesis, Eötvös Loránd University. Budapest., 1998.
16. L Praly. On observers with state independent error lyapunov function. In Proceedings of the 5th IFAC Symposium "Nonlinear Control Systems" (NOLCOS'01), 2001.
17. n. Kluwer Academic, 1997.
18. M. Spivak. (A Comprehensive Introduction to) Differential geometry, volume 2. Publish or Perish, Inc., 1979. 2nd Edition.
19. J. Tsinias. Further results on the observer design problem. Syst. Contr. Lett., 14:411-418, 1990.