Previous |  Up |  Next

Article

Keywords:
invariance; structure; stability; structural condition; Lyapunov function
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.
References:
[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 DOI 10.1109/9.788534 | MR 1709863 | Zbl 0958.93079
[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 DOI 10.1109/9.920793 | MR 1833028 | Zbl 1055.93064
[3] Bestle D., Zeitz M.: Canonical form observer design for non-linear time-variable systems. Internat. J. Control 38 (1983), 419–431 DOI 10.1080/00207178308933084 | MR 0708425
[4] Birk J., Zeitz M.: Extended Luenberger observer for non-linear multivariable systems. Internat. J. Control 47 (1988), 1823–1836 DOI 10.1080/00207178808906138 | MR 0947071
[5] Chiasson J. N., Novotnak R. T.: Nonlinear speed observer for the pm stepper motor. IEEE Trans. Automat. Control 38 (1993), 1584–1588 DOI 10.1109/9.241582 | MR 1242915
[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
[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
[8] Esfandiari F., Khalil H. K.: Output feedback stabilization of fully linearizable systems. Internat. J. Control 56 (1992), 1007–1037 DOI 10.1080/00207179208934355 | MR 1187838 | Zbl 0762.93069
[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 DOI 10.1109/TAC.1981.1102743 | MR 0635851 | Zbl 0553.93014
[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 DOI 10.1109/9.256352 | MR 1164571 | Zbl 0775.93020
[11] Glendinning P.: Stability, Instability and Chaos: An Introduction to the Theory of Nonlinear Differential Equations. Cambridge University Press, New York 1994 MR 1304054 | Zbl 0808.34001
[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 DOI 10.1109/9.489283 | MR 1385333 | Zbl 0851.93018
[13] Hrušák J.: Anwendung der Äquivalenz bei Stabilitätsprüfung, Tagung über die Regelungstheorie, Mathematisches Forschungsinstitut, Oberwolfach 196.
[14] Hrušák J., Černý V.: Non-linear and signal energy optimal asymptotic filter design. J. Systemics, Cybernetics and Informatics 1 (2003), 55–62
[15] Keller H.: Non-linear observer design by transformation into a generalized observer canonical form. Internat. J. Control 46 (1987), 1915–1930 DOI 10.1080/00207178708934024 | MR 0924264
[16] Krener A. J., Isidori A.: Linearization by output injection and nonlinear observers. Systems Control Lett. 3 (1983), 47–52 MR 0713426 | Zbl 0524.93030
[17] Krener A. J., Respondek W.: Nonlinear observers with linearizable error dynamics. SIAM J. Control Optim. 23 (1985), 197–216 DOI 10.1137/0323016 | MR 0777456 | Zbl 0569.93035
[18] Morales V. L., Plestan, F., Glumineau A.: Linearization by completely generalized input-output injection. Kybernetika 35 (1999), 793–802 MR 1747977
[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
[20] 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
[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 DOI 10.1016/0005-1098(93)90145-J | MR 1211308 | Zbl 0772.93017
[22] Rayleigh J. W.: The Theory of Sound. Dover Publications, New York 1945 MR 0016009 | Zbl 0061.45904
[23] Schwarz H. R.: Ein Verfahren zur Stabilitätsfrage bei Matrizen Eigenwertproblemen. Z. Angew. Math. Phys. 7 (1956), 473–500 DOI 10.1007/BF01601178 | MR 0083194
[24] Willems J. C.: Dissipative dynamical systems. Part I: general theory. Arch. Rational Mech. Anal. 45 (1972), 321–351 DOI 10.1007/BF00276493 | MR 0527462 | Zbl 0252.93003
[25] Zeitz M.: Observability canonical (phase-variable) form for non-linear time-variable systems. Internat. J. Control 15 (1984), 949–958 MR 0763769 | Zbl 0546.93011
[26] Zhou K., Doyle J. C.: Essentials of Robust Control. Prentice Hall, NJ 1998 Zbl 0890.93003
Partner of
EuDML logo