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On uniform observation of nonuniformly observable systems. (English) Zbl 0866.93013
Summary: Although observability of nonlinear systems is known to be dependent on the input, the proposed observers have the property that the estimation error decays to zero irrespective of the input. In the first part of this paper, it is shown that this phenomenon follows from a common property of these systems: for all of them, the “unobservable states” with respect to some input, are in some sense “stable” (in the linear case, these systems are called detectable), and for this reason, a reduced order observer can be designed. In the second part is given a more general class of nonlinear systems for which such an observer can be designed.

MSC:
93B07 Observability
93C10 Nonlinear systems in control theory
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[1] Besançon, G.; Hammouri, H., Reduced order observer for a class of non-uniformly observable systems, (), 121-125
[2] Bornard, G.; Couenne, N.; Celle, F., Regularly persistent observer for bilinear systems, () · Zbl 0676.93031
[3] Dawson, D.M.; Qu, Z.; Carroll, J.C., On the state observation and output feedback problems for nonlinear uncertain systems, Systems control lett., 18, 217-222, (1992) · Zbl 0752.93021
[4] Funahashi, Y., Stable state estimator for bilinear systems, Internat. J. control, 29, 181-188, (1979) · Zbl 0407.93045
[5] Gauthier, J.P.; Bornard, G., Observability for any u(t) of a class of nonlinear systems, IEEE trans. autom. control, 26, 922-926, (1981) · Zbl 0553.93014
[6] Gauthier, J.P.; Hammouri, H.; Othman, S., A simple observer for nonlinear systems — applications to bioreactors, IEEE trans. autom. control, 37, 875-880, (1992) · Zbl 0775.93020
[7] Hara, S.; Furuta, K., Minimal order state observers for bilinear systems, Internat. J. control, 24, 705-718, (1976) · Zbl 0336.93010
[8] Hermann, R.; Krener, A.J., Nonlinear controllability and observability, IEEE trans. autom. control, 22, 728-740, (1977) · Zbl 0396.93015
[9] Raghavan, S.; Hedrick, J.K., Observer design for a class of nonlinear systems, Internat. J. control, 59, 515-528, (1994) · Zbl 0802.93007
[10] Sussmann, H.J., Single input observability of continuous time systems, Math. systems theory, 12, 371-393, (1979) · Zbl 0422.93019
[11] Thau, F.E., Observing the state of nonlinear dynamic systems, Internat. J. control, 17, 471-479, (1973) · Zbl 0249.93006
[12] Walcott, B.L.; Zak, S.H., State observation of nonlinear uncertain dynamical systems, IEEE trans. autom. control, 32, 166-170, (1987) · Zbl 0618.93019
[13] Wonham, W.M., Linear multivariable control, (1985), Springer New York · Zbl 0314.93008
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