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design; nonlinear system; multi-input–multi-output system; backstepping approach; state affine systems; nonlinear equivalence
An observer design based on backstepping approach for a class of state affine systems is proposed. This class of nonlinear systems is determined via a constructive algorithm applied to a general nonlinear Multi Input–Multi Output systems. Some examples are given in order to illustrate the proposed methodology.
[1] Besançon G., Bornard, G., Hammouri H.: Observers synthesis for a class of nonlinear control systems. European J. Control (1996), 176–192 DOI 10.1016/S0947-3580(96)70043-2
[2] Busawon K., Farza, M., Hammouri H.: Observers’ synthesis for a class of nonlinear systems with application to state and parameter estimation in bioreactors. In: Proc. 36th IEEE Conference on Decision and Control, San Diego, California 1997
[3] Busawon K., Saif M.: An Observer for a class disturbance driven nonlinear systems. Appl. Math. Lett. 11 (1998), 6, 109–113 DOI 10.1016/S0893-9659(98)00111-6 | MR 1647133
[4] Conte G., Moog C. H., Perdon A. M.: Nonlinear Control Systems – An algebraic setting. Springer–Verlag, Berlin 1999 MR 1687965 | Zbl 0920.93002
[5] Diop S.: Elimination in control theory. Math. Control Signals Systems 4 (1991), 17–32 DOI 10.1007/BF02551378 | MR 1082853 | Zbl 0727.93025
[6] Diop S., Fliess M.: On nonlinear observability. In: Proc. European Control Conference (ECC’91), Grenoble 1991
[7] Gauthier J. P., Bornard G.: Observability for any $u(t)$ of a class of nonlinear systems. IEEE Trans. Automat. Control 26 (1981), 922–926 DOI 10.1109/TAC.1981.1102743 | MR 0635851 | Zbl 0553.93014
[8] Gauthier J. P., Kupka I.: Observability and observers for nonlinear systems. SIAM J. Control Optim. 32 (1994), 4, 974–994 DOI 10.1137/S0363012991221791 | MR 1280224 | Zbl 0802.93008
[9] Glumineau A., Moog C. H., Plestan F.: New algebro-geometric conditions for the linearization by input-output injection. IEEE Trans. Automat. Control 41 (1996), 598–603 DOI 10.1109/9.489283 | MR 1385333 | Zbl 0851.93018
[10] Hammouri H., Gauthier: Global time varying linearization up to output injection. SIAM J. Control Optim. 30 (1992), 1295–1310 DOI 10.1137/0330068 | MR 1185623 | Zbl 0771.93033
[11] Hammouri H., Morales J. De Leon: Observer Synthesis for state affine systems. In: Proc. 29th IEEE Conference on Decision and Control, Honolulu 1990, pp. 784–785
[12] Kang W., Krener A. J.: Nonlinear asymptotic observer design: A backstepping approach. In: AFOSR Workshop on Dynamics Systems and Control, Pasadena, California 1998
[13] Krener A. J., Isidori A.: Linearization by output injection and nonlinear observers. Systems Control Lett. 3 (1983), 47–52 MR 0713426 | Zbl 0524.93030
[14] López–M. V., Morales, J. de Léon, Glumineau A.: Transformation of nonlinear systems into state affine control systems and observer synthesis. In: IFAC CSSC, Nantes 1998, pp. 771–776
[15] López–M. V., Plestan, F., Glumineau A.: Linearization by completely generalized input-output injection. Kybernetika 35 (1999), 6, 793–802 MR 1747977
[16] Plestan F., Glumineau A.: Linearization by generalized input output injection. Systems Control Lett. 31 (1997), 115–128 DOI 10.1016/S0167-6911(97)00025-X | MR 1461807 | Zbl 0901.93013
[17] Souleiman I., Glumineau A.: Constructive transformation of nonlinear systems into state affine MIMO form and nonlinear observers. Internat. J. Control. Submitted
[18] Nijmeijer H., (eds.) T. I. Fossen: New Directions in Nonlinear Observer Design (Lecture Notes in Control and Inform. Sciences 244). Springer–Verlag, Berlin 1999 MR 1699373
[19] Schaft A. J. Van der: Representing a nonlinear state space system as a set of higher order differential equations in the inputs and outputs. Systems Control Lett. 12 (1989), 151–160 DOI 10.1016/0167-6911(89)90008-X | MR 0985565
[20] Xia X. H., Gao W. B.: Nonlinear observer design by observer error linearization. SIAM J. Control Optim. 1 (1989), 199–216 MR 0980230 | Zbl 0667.93014
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