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Keywords:
nonlinear control system; time delay; observability
nonlinear control system; time delay; observability
Summary:
Basic properties on linearization by output injection are investigated in this paper. A special structure is sought which is linear up to a suitable output injection and under a suitable change of coordinates. It is shown how an observer may be designed using theory available for linear time delay systems.
References:
[1] Aggoune W., Bouteayeb, M., Darouach M.: Observers design for a class of nonlinear systems with time-varying delay. In: Proc. 38th IEEE Conference on Decision and Control, Phoenix 1999
[2] Antoniades C., Christofides D.: Robust control of nonlinear time-delay systems. Internat. J. Math. Comp. Sci. 9 (1999), 4, 811–837 MR 1736672 | Zbl 0952.93042
[3] Bocharov G. A., Rihan F. A.: Numerical modelling in biosciences using delay differential equations. J. Comput. Appl. Math. 125 (2000), 183–199 DOI 10.1016/S0377-0427(00)00468-4 | MR 1803191 | Zbl 0969.65124
[4] Conte G., Perdon A. M.: The disturbance decoupling problem for systems over a ring. SIAM J. Control Optim. 33 (1995), 3, 750–764 DOI 10.1137/S0363012992235638 | MR 1327237 | Zbl 0831.93011
[5] Fliess M., Mounier H.: Controllability and observability of linear delay systems: an algebraic approach. ESIAM: Control, Optimization & Calculus of Variations 3 (1998), 301–314 MR 1644427 | Zbl 0908.93013
[6] Germani A., Manes, C., Pepe P.: Linearization of input–output mapping for nonlinear delay systems via static state feedback. In: Symposium on Modeling Analysis & Sim., Lille 1997, pp. 599–602
[7] Germani A., Manes, C., Pepe P.: Local asymptotic stability for nonlinear state feedback delay systems. In: Proc. 6th IEEE Mediteranean Conference on Control Systems, Alghero 1998 MR 1760886
[8] Hale J.: Theory of Functional Differential Equations. Springer–Verlag, Berlin 1977 MR 0508721 | Zbl 1092.34500
[9] Hale J., Verduyn S. M.: Introduction to Functional Differential Equations. Springer–Verlag, Berlin 1993 MR 1243878 | Zbl 0787.34002
[10] He J.-B., Wang Q.-G., Lee T.-H.: PI/PID controller tuning via LQR approach. Chem. Engrg. Sci. 55 (2000), 2429–2439 DOI 10.1016/S0009-2509(99)00512-6
[11] Kolmanovskii V. B., Nosov V. R.: Stability of Functional Differential Equations. Academic Press, London 1986 MR 0860947 | Zbl 0593.34070
[12] Kolmanovskii V. B., Richard J. P., Tchangani A. Ph.: Some model transformations for the stability study of linear systems with delay. In: Preprints of the 1st IFAC Internat. Workshop on Linear Time-Delay Systems (J. M. Dion, L. Dugard, and M. Fliess, eds.), Lag 1998, pp. 75–80 MR 1622951
[13] Krener A., Isidori A.: Linearization by output injection and nonlinear observers. Systems Control Lett. 3 (1983), 47–52 MR 0713426 | Zbl 0524.93030
[14] Krener A., Respondek W.: Nonlinear observers with linearizable error dynamics. SIAM J. Control Optim. 23 (1985), 2, 197–216 DOI 10.1137/0323016 | MR 0777456 | Zbl 0569.93035
[15] Lee E. B., Olbrot A.: Observability and related structural results for linear hereditary systems. Internat. J. Control 34 (1981), 6, 1061–1078 DOI 10.1080/00207178108922582 | MR 0643872 | Zbl 0531.93015
[16] Lee Y., Lee, J., Park S.: PID controller tuning for integrating and unstable PI processes with time delay. Chem. Engrg. Sci. 55 (2000), 3481–3493 DOI 10.1016/S0009-2509(00)00005-1
[17] Malek–Zavarei M., Jamshidi M.: Time–Delay Systems. Analysis, Optimization and Applications. (North Holland Systems and Control Series 9.) Elsevier, New York 1987 MR 0930450 | Zbl 0658.93001
[18] Márquez–Martínez L. A., Moog C. H.: New results on the analysis and control of nonlinear time-delay systems. In: Proc. 38th IEEE Conference on Decision and Control, Phoenix 1999
[19] Márquez–Martínez L. A., Moog C. H.: Accessibility and Feedback Linearization of Nonlinear Time-Delay Systems. Technical Report, IRCCyN 2000
[20] Márquez–Martínez L. A., Moog C. H.: Accessibility of nonlinear time-delay systems. In: Proc. 40th IEEE Conference on Decision and Control 2001
[21] Moog C. H., Castro–Linares R., Velasco–Villa, M., Márquez–Martínez L. A.: Disturbance decoupling for time-delay nonlinear systems. IEEE Trans. Automat. Control 48 (2000), 2, 305–309 DOI 10.1109/9.839954
[22] Picard P.: Sur l’observabilité et la commande des systèmes linéaires à retards modelisés sur un anneau. Ph.D. Thesis. Université de Nantes 1996
[23] Plestan F.: Linéarisation par injection d’entrée–sortie généralisée et synthèse d’observateurs. Ph.D. Thesis. Université de Nantes / Ecole Centrale de Nantes 1995
[24] Xia X., Moog C. H.: I/O linearization of nonlinear systems by output feedback. In: Proc. 35th IEEE Conference on Decision and Control, Kobe 1996
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