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structure at infinity; row-by-row decoupling; delay systems
We consider the row-by-row decoupling problem for linear delay systems and show some close connections between the design of a decoupling controller and some particular structures of delay systems, namely the so-called weak structure at infinity. The realization by static state feedback of decoupling precompensators is studied, in particular, generalized state feedback laws which may incorporate derivatives of the delayed new reference.
[1] Commault C., Dion J.-M., Descusse J., Lafay J. F., Malabre M.: Influence de la structure à l’infini des systèmes linéaires sur la résolution de problèmes de commande. Autom. Prod. Inform. Indust. (Automatic Control-Production Systems) 20 (1986), 207–252 MR 0846163
[2] Descusse J., Dion J.-M.: On the structure at infinity of linear square decoupled systems. IEEE Trans. Automat. Control AC-27 (1982), 971–974 DOI 10.1109/TAC.1982.1103041 | MR 0680500 | Zbl 0485.93042
[3] Falb P. L., Wolovich W. A.: Decoupling in the design and synthesis of multivariable control systems. IEEE Trans. Automat. Control AC-12 (1967), 651–659 DOI 10.1109/TAC.1967.1098737
[4] Hautus M. L. J.: The formal Laplace transform for smooth linear systems. In: Proc. Internat. Symposium on Mathematical Systems Theory, Udine, Italy, June 1975 (Lecture Notes in Economics and Mathematical Systems 131), Springer-Verlag, Berlin 1975, pp. 29–47 MR 0682787
[5] Hautus M. L. J.: $(A,B)$-invariant and stabilizability subspaces, a frequency domain description. Automatica 16 (1980), 703–707 DOI 10.1016/0005-1098(80)90012-6 | MR 0607188 | Zbl 0455.93015
[6] Kailath T.: Linear System. Prentice Hall, Englewood Cliffs, N. J. 1980 MR 0569473 | Zbl 0458.93025
[7] Malabre M., Kučera V.: Infinite structure and exact model matching: a geometric approach. IEEE Trans. Automat. Control AC-29 (1984), 226–268 DOI 10.1109/TAC.1984.1103502
[8] Malabre M., Martínez-García: The modified disturbance rejection problem with stability: a structural approach. In: Proc. European Control Conference 2 (1993), pp. 1119–1124
[9] Malabre M., Rabah R.: On infinite zeros for infinite dimensional systems. In: Progress in Systems and Control Theory 3, Realiz. Model. in Syst. Theory, Vol. 1, Birkhaüser, Boston 1990, pp. 19–206 MR 1115331
[10] Malabre M., Rabah R.: Structure at infinity, model matching and disturbance rejection for linear systems with delays. Kybernetika 29 (1993), 485–498 MR 1264881 | Zbl 0805.93008
[11] Picard P., Lafay J. F., Kučera V.: Model matching for linear systems with delays. In: Proc. 13th IFAC Congress, San Francisco, Volume D, 1996, pp. 183–188
[12] Rabah R., Malabre M.: Structure at infinity for delay systems revisited. In: IMACS and IEEE-SMC Multiconference CESA’96, Symposium on Modelling, Analysis and Simulation, Lille, France, July 9–12, 1996, pp. 87–90
[13] Rabah R., Malabre M.: A note on decoupling for linear infinite dimensional systems. In: Proc. 4th IFAC Conference on System Structure and Control, Bucharest, October 23–25, 1997, pp. 78–83
[14] Rabah R., Malabre M.: On the structure at infinity of linear delay systems with application to the disturbance decoupling problem. Kybernetika 35 (1999), 668–680 MR 1747968
[15] Rekasius Z. V., Milzareck R. J.: Decoupling without prediction of systems with delays. In: Proc. Joint Automat. Control Conference, San Francisco, CA, 1977
[16] Sename O., Rabah, R., Lafay J. F.: Decoupling without prediction of linear systems with delays: a structural approach. System Control Lett. 25 (1995), 387–395 DOI 10.1016/0167-6911(94)00086-B | MR 1343224 | Zbl 0877.93053
[17] Silverman L. M., Kitapçi A.: System structure at infinity. In: Outils et Modèles Mathématiques pour l’Automatique, l’Analyse des Systèmes et le Traitement du Signal, Vol. 3, Colloque National, Belle-Ile, 13–18 septembre, Ed. CNRS, Paris 1983, pp. 413–424 MR 0733951 | Zbl 0529.93018
[18] Tzafestas S. G., Paraskevopoulos P. N.: On the decoupling of multivariable control systems with time-delays. Internat. J. Control 17 (1973), 405–415 DOI 10.1080/00207177308932387 | MR 0314498 | Zbl 0246.93023
[19] Tsoi A. C.: Recent advances in the algebraic system theory of delay differential equations. In: Recent Theoretical Developments in Control (M. J. Gregson, ed.), Academic Press, New York 1978, pp. 67–127 MR 0534622 | Zbl 0417.93003
[20] Wonham W. M.: Linear Multivariable Control: A Geometric Approach. Springer–Verlag, New York 1985 MR 0770574 | Zbl 0609.93001
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