Observability and observers for nonlinear systems with time delays
Kybernetika, Tome 38 (2002) no. 4, pp. 445-456 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 93B07, 93B18, 93C10, 93C23
Keywords: nonlinear control system; time delay; observability
@article{KYB_2002_38_4_a3,
     author = {M\'arquez-Mart{\'\i}nez, Luis Alejandro and Moog, Claude H. and Velasco-Villa, Mart{\'\i}n},
     title = {Observability and observers for nonlinear systems with time delays},
     journal = {Kybernetika},
     pages = {445--456},
     year = {2002},
     volume = {38},
     number = {4},
     mrnumber = {1937139},
     zbl = {1265.93060},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2002_38_4_a3/}
}
TY  - JOUR
AU  - Márquez-Martínez, Luis Alejandro
AU  - Moog, Claude H.
AU  - Velasco-Villa, Martín
TI  - Observability and observers for nonlinear systems with time delays
JO  - Kybernetika
PY  - 2002
SP  - 445
EP  - 456
VL  - 38
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/KYB_2002_38_4_a3/
LA  - en
ID  - KYB_2002_38_4_a3
ER  - 
%0 Journal Article
%A Márquez-Martínez, Luis Alejandro
%A Moog, Claude H.
%A Velasco-Villa, Martín
%T Observability and observers for nonlinear systems with time delays
%J Kybernetika
%D 2002
%P 445-456
%V 38
%N 4
%U http://geodesic.mathdoc.fr/item/KYB_2002_38_4_a3/
%G en
%F KYB_2002_38_4_a3
Márquez-Martínez, Luis Alejandro; Moog, Claude H.; Velasco-Villa, Martín. Observability and observers for nonlinear systems with time delays. Kybernetika, Tome 38 (2002) no. 4, pp. 445-456. http://geodesic.mathdoc.fr/item/KYB_2002_38_4_a3/

[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 | Zbl

[3] Bocharov G. A., Rihan F. A.: Numerical modelling in biosciences using delay differential equations. J. Comput. Appl. Math. 125 (2000), 183–199 | DOI | MR | Zbl

[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 | MR | Zbl

[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 | Zbl

[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

[8] Hale J.: Theory of Functional Differential Equations. Springer–Verlag, Berlin 1977 | MR | Zbl

[9] Hale J., Verduyn S. M.: Introduction to Functional Differential Equations. Springer–Verlag, Berlin 1993 | MR | Zbl

[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

[11] Kolmanovskii V. B., Nosov V. R.: Stability of Functional Differential Equations. Academic Press, London 1986 | MR | Zbl

[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

[13] Krener A., Isidori A.: Linearization by output injection and nonlinear observers. Systems Control Lett. 3 (1983), 47–52 | MR | Zbl

[14] Krener A., Respondek W.: Nonlinear observers with linearizable error dynamics. SIAM J. Control Optim. 23 (1985), 2, 197–216 | DOI | MR | Zbl

[15] Lee E. B., Olbrot A.: Observability and related structural results for linear hereditary systems. Internat. J. Control 34 (1981), 6, 1061–1078 | DOI | MR | Zbl

[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

[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 | Zbl

[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

[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