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State observers for a class of multi-output nonlinear dynamic systems. (English) Zbl 1221.93035
Summary: This note considers the problem of observer design for a class of multi-output nonlinear systems. A new state observer design methodology for linear time-varying multi-output systems is presented. Furthermore, we show that the same methodology can be extended to a class of multi-output nonlinear systems. Some sufficient conditions for the existence of the proposed observer are obtained, which guarantee that the error of state estimation converges asymptotically to zero. An example is given to demonstrate the effectiveness of the proposed methodology.

MSC:
93B07 Observability
93C10 Nonlinear systems in control theory
34H05 Control problems involving ordinary differential equations
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[1] Bestle, D.; Zeitz, M., Canonical form observer design for nonlinear time-variable systems, International journal of control, 38, 419-431, (1983) · Zbl 0521.93012
[2] Krener, A.J.; Isidori, A., Linearization by output injection and nonlinear observers, Systems & control letters, 3, 47-52, (1983) · Zbl 0524.93030
[3] Gauthier, J.P.; Kupka, I., A separation principle for bilinear systems with dissipative drift, IEEE transactions on automatic control, 37, 1970-1974, (1992) · Zbl 0778.93102
[4] Bornard, G.; Couenne, N.; Celle, F., Regularly persistent observers for bilinear systems, New trends in nonlinear control theory, 122, 130-140, (1989) · Zbl 0676.93031
[5] Aurora, C.; Ferrara, A., A sliding mode observer for sensorless induction motor speed regulation, International journal of systems science, 38, 913-929, (2007) · Zbl 1160.93303
[6] Ibrir, S., On observer design for nonlinear systems, International journal of systems science, 37, 1097-1109, (2006) · Zbl 1111.93009
[7] Mishkov, R.L., Nonlinear observer design by reduced generalized observer canonical form, International journal of control, 78, 172-185, (2005) · Zbl 1098.93007
[8] Pertew, A.M.; Marquez, H.J.; Zhao, Q., \(H_\infty\) observer design for Lipschitz nonlinear systems, IEEE transactions on automatic control, 51, 1211-1216, (2006) · Zbl 1366.93162
[9] Gauthier, J.P.; Kupka, I.A.K., Observability and observers for nonlinear systems, SIAM journal on control and optimization, 32, 975-994, (1994) · Zbl 0802.93008
[10] Noh, D.; Jo, N.H.; Seo, J.H., Nonlinear observer design by dynamic observer error linearization, IEEE transactions on automatic control, 49, 1746-1750, (2004) · Zbl 1365.93060
[11] Kreisselmeier, G.; Engel, R., Nonlinear observers for autonomous Lipschitz continuous systems, IEEE transactions on automatic control, 48, 451-464, (2003) · Zbl 1364.93093
[12] Califano, C.; Monaco, S.; Normand-Cyrot, D., Canonical observer forms for multi-output systems up to coordinate and output transformations in discrete time, Automatica, 45, 2483-2490, (2009) · Zbl 1183.93044
[13] Zhao, Y.; Tao, J.; Shi, N., A note on observer design for one-sided Lipschitz nonlinear systems, Systems & control letters, 59, 66-71, (2010) · Zbl 1186.93017
[14] Dong, Y.; Mei, S., Adaptive observer for a class of nonlinear systems, Acta automatica sinica, 33, 10, 1081-1084, (2007)
[15] Dong, Y., New methodology for observer design of a class of nonlinear systems, Journal of systems engineering and electronics, 31, 153-157, (2009)
[16] Busawon, K.K.; Saif, M., A state observer for nonlinear systems, IEEE transactions on automatic control, 44, 2098-2103, (1999) · Zbl 1136.93312
[17] Hu, G., Observers for one-sided Lipschitz non-linear systems, IMA journal of mathematical control and information, 23, 395-401, (2006) · Zbl 1113.93021
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