Abstract
A NSC for the transformation to the state affine systems of MISO nonlinear systems has been obtained. The main result is stated in terms of the I/O differential equation and some one-forms obtained in a straightforward way and easy to check. With the help of a regular transformation, one avoids the time varying computation of the observer gain matrice an then a Kalmanlike observer Σo (4.3) for the transformed system Σa (4.2) can be directly applied.
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G. Besançon and G. Bornard. State equivalence based observer synthesis for nonlinear control systems. Proc. IFAC 13th Triennial World Congress, (San Francisco, USA, Vol. E, 287–292, 1996.
J. Birk and M. Zeitz. Extended Luenberger observer for nonlinear multivariable systems, Int. J. Control, 47, 1823–1836, 1988.
G. Bornard, N. Couenne and F. Celle. Regularly persistent observers for bilinear systems Proc. in 29 I.C.N.S., New trends in nonlinear system theory, (Vol. 122 Springer Verlag) June 1988.
K. Busawon, M. Farza and H. Hammouri. A simple observer for a class of nonlinear systems, Personal Communication.
J. N. Chiasson. ‘Nonlinear differential-geometric techniques for control of a series DC motor', IEEE Trans. Contr. Syst. Technology, 2, 35–42, 1994.
S. Diop, J. W. Grizzle, P. E. Moraal and A. Stefanopoulou. Interpolation and numerical differentiation for observer design, Proc. ACC 94, Evanston, Illinois, 1329–1333, 1994.
J. P. Gauthier, H. Hammouri and S. Othman. A simple observer for nonlinear systems applications to bioreactors. IEEE TAC, 37(6), 885–880, 1992.
D. Guillaume, P. Rouchon and J. Rudolph. Two simple observers for a class of polymerization reactors, 4 th ECC’ 97, Bruxelles, 1997.
A. Glumineau, C. H. Moog and F. Plestan. New algebro-geometric conditions for the linearization by input-output injection, IEEE Trans. Autom. Control, 41, 598–603, 1996.
H. Hammouri and J. P. Gauthier. Bilinearization up to output injection, Syst. Contr. Letters, 11, 139–149, 1988.
H. Hammouri and J. P. Gauthier. Global time varying linearization up to output injection, SIAM J. Control Optim., 30 1992, 1295–1310, 1992.
H. Hammouri and M. de León. Observer synthesis for state-affine systems, 29 th. CDC, Honolulu, Hawai. Dec. 5–7, 1990.
H. Hammouri and M. de León. On systems equivalence and observer synthesis. New Trends in Systems Theory, 340–347, 1991.
H. Hammouri and M. Kinnaert. A new procedure for time-varying linearization up to output injection, Syst. Contr. Lett., 28, 151–157, 1996.
H. Keller. ‘Nonlinear observer design by transformation into a generalized observer canonical form', Int. J. Control, 46, 1915–1930, 1987.
A. J. Krener and W. Respondek. Nonlinear observers with linearizable error dynamics, SIAM J. Contr. Optim., 23, 197–216, 1985.
J. de León Morales and S. Acha Daza. Stabilization of a class of nonlinear systems, application to a synchronous generator, Proc. of IASTE Int. Conf. High technology in the Power Industry, Orlando Fl., USA, 23–26, 1998.
J. Lévine and R. Marino, Nonlinear systems immersion, observers and finite dimensional filters, Syst. Contr. Lett., 7 (1986), 133–142.
V. López-M. and A. Glumineau. ‘Further results on linearization of nonlinear systems by input output injection', Proc. 36th. CDC IEEE, (San Diego, USA), 1997.
V. López-M. and J. de León Morales and A. Glumineau. Transformation of nonlinear systems into state affine control systems and observer synthesis, IFAC CSSC, Nantes, France, July 8–10, 1998.
V. López-M., F. Plestan and A. Glumineau. Linearization by completely generalized input-output injection, Proc. of 6 th IEEE MCCA, Alghero, Italy, 9–11, 1998.
R. Marino and P. Tomei. ‘Dynamic output feedback linearization and global stabilization', Syst. Contr. Letters, 17, 115–121, 1991.
F. Plestan and B. Cherki. ‘An observer for a one flexible joint robot by an algebraic method', Proc. IFAC Workshop on New Trends in Design of Control Systems NTDCS'94 (Smolenice, Slovakia), 41–46, 1994.
F. Plestan and A. Glumineau. ‘Linearization by generalized input-output injectionĂ for electrical motor observers', Electrimacs 96 (Saint Nazaire, France), 2/3, 569–574, 1996.
F. Plestan and A. Glumineau. ‘Linearization by generalized input-output injection', Syst. Contr. Letters, 31, 115–128, 1997.
T. Proychev and R. L. Mishkov. ‘Transformation of nonlinear systems in observer canonical form with reduced dependency on derivatives of the input', Automatica, 29, 495–498, 1993.
J. Tsinias. Further results on the observer design problem, Syst. Contr. Lett., 14, 411–418, 1990.
D. Williamson. Observation of bilinear systems with application to biological systems, Automatica, 13, 243–254, 1977.
A. J. Van der Schaft. Representing a nonlinear state space system as a set of higher-order differential equations in the inputs and outputs, Syst. Contr. Lett., 12, 151–160, 1989.
F. Viel. Stabilité des systèmes controlés par retour d'état estimé. Application aux réacteurs de polymérisation et aux colonnes à distiller, Thèse de Doctorat, Université Claude Bernard-Lyon 1, Lyon, 1994.
X. H. Xia and W. B. Gao. Nonlinear observer design by observer error linearization, SIAM J. Contr. Optim., 1, 199–216, 1989.
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© 1999 Springer-Verlag London Limited
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Glumineau, A., López-M., V. (1999). Transformation to state affine system and observer design. In: Nijmeijer, H., Fossen, T. (eds) New Directions in nonlinear observer design. Lecture Notes in Control and Information Sciences, vol 244. Springer, London. https://doi.org/10.1007/BFb0109921
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DOI: https://doi.org/10.1007/BFb0109921
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