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Title: Non-linear observer design method based on dissipation normal form (English)
Author: Černý, Václav
Author: Hrušák, Josef
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 41
Issue: 1
Year: 2005
Pages: [59]-74
Summary lang: English
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Category: math
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Summary: Observer design is one of large fields investigated in automatic control theory and a lot of articles have already been dedicated to it in technical literature. Non-linear observer design method based on dissipation normal form proposed in the paper represents a new approach to solving the observer design problem for a certain class of non-linear systems. As the theoretical basis of the approach the well known dissipative system theory has been chosen. The main achievement of the contribution consists in the fact that the error dynamics of the observer is priory chosen non-linear. It provides more flexibility in the sense of specifying error convergence properties to zero in comparison with other techniques. Lyapunov’s stability theory is the other basic point of the approach. (English)
Keyword: invariance
Keyword: structure
Keyword: stability
Keyword: structural condition
Keyword: Lyapunov function
MSC: 93B07
MSC: 93B50
MSC: 93C10
idZBL: Zbl 1249.93021
idMR: MR2131125
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Date available: 2009-09-24T20:06:54Z
Last updated: 2015-03-23
Stable URL: http://hdl.handle.net/10338.dmlcz/135639
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Reference: [1] Atassi A. N., Khalil H. K.: A separation principle for the stabilization of a class of nonlinear systems.IEEE Trans. Automat. Control 44 (1999), 1672–1687 Zbl 0958.93079, MR 1709863, 10.1109/9.788534
Reference: [2] Atassi A. N., Khalil H. K.: A separation principle for the control of a class of nonlinear systems.IEEE Trans. Automat. Control 46 (2001), 742–746 Zbl 1055.93064, MR 1833028, 10.1109/9.920793
Reference: [3] Bestle D., Zeitz M.: Canonical form observer design for non-linear time-variable systems.Internat. J. Control 38 (1983), 419–431 MR 0708425, 10.1080/00207178308933084
Reference: [4] Birk J., Zeitz M.: Extended Luenberger observer for non-linear multivariable systems.Internat. J. Control 47 (1988), 1823–1836 MR 0947071, 10.1080/00207178808906138
Reference: [5] Chiasson J. N., Novotnak R. T.: Nonlinear speed observer for the pm stepper motor.IEEE Trans. Automat. Control 38 (1993), 1584–1588 MR 1242915, 10.1109/9.241582
Reference: [6] Černý V., Hrušák J.: Separation principle for a class of non-linear systems.In: Proc. 11th IEEE Mediterranean Conference on Control and Automation, Rhodes 2003
Reference: [7] Černý V., Hrušák J.: On some new similarities between nonlinear observer and filter design.In: Preprints 6th IFAC Symposium on Nonlinear Control Systems, Vol. 2, Stuttgart 2004, pp. 609–614
Reference: [8] Esfandiari F., Khalil H. K.: Output feedback stabilization of fully linearizable systems.Internat. J. Control 56 (1992), 1007–1037 Zbl 0762.93069, MR 1187838, 10.1080/00207179208934355
Reference: [9] Gauthier J. P., Bornard G.: Observability for any $u(t)$ of a class of nonlinear systems.IEEE Trans. Automat. Control 26 (1981), 922–926 Zbl 0553.93014, MR 0635851, 10.1109/TAC.1981.1102743
Reference: [10] Gauthier J. P., Hammouri, H., Othman S.: A simple observer for nonlinear systems applications to bioreactors.IEEE Trans. Automat. Control 37 (1992), 875–880 Zbl 0775.93020, MR 1164571, 10.1109/9.256352
Reference: [11] Glendinning P.: Stability, Instability and Chaos: An Introduction to the Theory of Nonlinear Differential Equations.Cambridge University Press, New York 1994 Zbl 0808.34001, MR 1304054
Reference: [12] 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 Zbl 0851.93018, MR 1385333, 10.1109/9.489283
Reference: [13] Hrušák J.: Anwendung der Äquivalenz bei Stabilitätsprüfung, Tagung über die Regelungstheorie, Mathematisches Forschungsinstitut, Oberwolfach 196.
Reference: [14] Hrušák J., Černý V.: Non-linear and signal energy optimal asymptotic filter design.J. Systemics, Cybernetics and Informatics 1 (2003), 55–62
Reference: [15] Keller H.: Non-linear observer design by transformation into a generalized observer canonical form.Internat. J. Control 46 (1987), 1915–1930 MR 0924264, 10.1080/00207178708934024
Reference: [16] Krener A. J., Isidori A.: Linearization by output injection and nonlinear observers.Systems Control Lett. 3 (1983), 47–52 Zbl 0524.93030, MR 0713426
Reference: [17] Krener A. J., Respondek W.: Nonlinear observers with linearizable error dynamics.SIAM J. Control Optim. 23 (1985), 197–216 Zbl 0569.93035, MR 0777456, 10.1137/0323016
Reference: [18] Morales V. L., Plestan, F., Glumineau A.: Linearization by completely generalized input-output injection.Kybernetika 35 (1999), 793–802 MR 1747977
Reference: [19] Patel M. R., Fallside, F., Parks P. C.: A new proof of the Routh and Hurwitz criterion by the second method of Lyapunov with application to optimum transfer functions.IEEE Trans. Automat. Control 9 (1963), 319–322
Reference: [20] Plestan F., Glumineau A.: Linearization by generalized input-output injection.Systems Control Lett. 31 (1997), 115–128 Zbl 0901.93013, MR 1461807, 10.1016/S0167-6911(97)00025-X
Reference: [21] Proychev T. Ph., Mishkov R. L.: Transformation of nonlinear systems in observer canonical form with reduced dependency on derivatives of the input.Automatica 29 (1993), 495–498 Zbl 0772.93017, MR 1211308, 10.1016/0005-1098(93)90145-J
Reference: [22] Rayleigh J. W.: The Theory of Sound.Dover Publications, New York 1945 Zbl 0061.45904, MR 0016009
Reference: [23] Schwarz H. R.: Ein Verfahren zur Stabilitätsfrage bei Matrizen Eigenwertproblemen.Z. Angew. Math. Phys. 7 (1956), 473–500 MR 0083194, 10.1007/BF01601178
Reference: [24] Willems J. C.: Dissipative dynamical systems.Part I: general theory. Arch. Rational Mech. Anal. 45 (1972), 321–351 Zbl 0252.93003, MR 0527462, 10.1007/BF00276493
Reference: [25] Zeitz M.: Observability canonical (phase-variable) form for non-linear time-variable systems.Internat. J. Control 15 (1984), 949–958 Zbl 0546.93011, MR 0763769
Reference: [26] Zhou K., Doyle J. C.: Essentials of Robust Control.Prentice Hall, NJ 1998 Zbl 0890.93003
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