Observer design for nonlinear systems. (English) Zbl 0684.93006

Tsinias, John

Syst. Control Lett. 13, No. 2, 135-142 (1989).

Summary: This paper deals with the observer design problem of a wide class of nonlinear systems subjected to bounded nonlinearities. A sufficient Lyapunov-like condition is provided and the proposed dynamic observer is a direct extension of the one in linear case.

MSC:

93B07	Observability
93C10	Nonlinear systems in control theory
93B50	Synthesis problems

Keywords:

observer design; bounded nonlinearities; Lyapunov-like condition

References:

[1]	Andreini, A.; Bacciotti, A.; Stefani, G., Global stabilizability of homogeneous vectors fields of odd degree, Systems Control Lett., 10, 251-256 (1988) · Zbl 0653.93040
[2]	Baumann, W.; Rugh, W., Feedback control of nonlinear systems by extended linearization, IEEE Trans. Automat. Control, 31, 40-47 (1986) · Zbl 0582.93031
[3]	Bestle, D.; Zeitz, M., Canonical form observer design for non-linear time variable systems, Internat. J. Control, 38, 419-431 (1983) · Zbl 0521.93012
[4]	Corless, M. J.; Leitmann, G., Continuous state feedback guaranteering uniform ultimate boundedness for uncertain dynamic systems, IEEE Trans. Automat. Control, 26, 1139-1144 (1981) · Zbl 0473.93056
[5]	Derese, I. A., Bilinear Observers for bilinear systems, IEEE Trans. Automat. Control, 26, 590-592 (1981) · Zbl 0488.93010
[6]	Gauthier, J. P.; Kazakos, D., Observability and observers for non-linear systems, (Proc. 25th Conf. Decision Contr.. Proc. 25th Conf. Decision Contr., Athens (1986)) · Zbl 0635.93013
[7]	Grassall, O. M.; Isidori, A., An existence theorem for observers of bilinear systems, IEEE Trans. Automat. Control, 26, 1299-1300 (1981) · Zbl 0479.93015
[8]	Hammouri, H.; Gauthier, J. O., Bilinearization up to output injection, Systems Control Lett., 11, 139-149 (1988) · Zbl 0648.93024
[9]	Kou, S. R.; Elliot, D. L.; Tarn, T. J., Exponential observers for nonlinear dynamic systems, Internat. J. Control, 29, 204-216 (1975) · Zbl 0319.93049
[10]	Krener, A. J.; Respondek, W., Nonlinear observers and linearizable error dynamics, SIAM J. Control Optim., 23, 197-216 (1985) · Zbl 0569.93035
[11]	Levine, J.; Marino, R., Nonlinear system immersion, observers and finite-dimensional filters, Systems Control Lett., 7, 133-142 (1986) · Zbl 0592.93030
[12]	Nicosia, S.; Tomei, P.; Tornambé, A., Approximate asymptotic observers for a class of nonlinear systems, (Proc. of the 26th CDC. Proc. of the 26th CDC, Los Angeles (1986)), 157-162
[13]	Selgrade, J. F., Asymptotic behavior of solutions to single loop positive feedback systems, J. Differential Equations, 38, 88-103 (1980) · Zbl 0419.34054
[14]	van der Schaft, A. J., On nonlinear observers, IEEE Trans. Automat. Control, 30, 1254-1256 (1986) · Zbl 0578.93009
[15]	Tsinias, J., Stabilization of affine in control nonlinear systems, Nonlinear Anal., 12, 1283-1296 (1988) · Zbl 0662.93055
[16]	Tsinias, J.; Kalouptsidis, N., Prolongations and stability analysis via Liapunov functions of dynamical polysystems, Math. Systems Theory, 20, 215-233 (1987) · Zbl 0642.93052
[17]	Walcott, B. L.; Zak, S. H., State observation of nonlinear uncertain dynamical systems, IEEE Trans. Automat. Control, 32, 166-170 (1987) · Zbl 0618.93019
[18]	Willems, J. C., Stability Theory of Dynamical Systems (1970), Wiley: Wiley New York · Zbl 0222.93010
[19]	Williamson, D., Observation of bilinear systems with application to biological control, Automatica, 13, 243-254 (1977) · Zbl 0351.93008
[20]	Wonham, W. M., Linear Multivariable Control (1979), Springer: Springer New York · Zbl 0393.93024
[21]	Xia, X.; Gao, W., On exponential observers for nonlinear systems, Systems Control Lett., 11, 319-325 (1988) · Zbl 0654.93010