Geodesic
On the regulator problem for a class of LTI systems with delays
Kybernetika, Tome 39 (2003) no. 4, pp. 415-432 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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This paper deals with the problem of tracking a reference signal while maintaining the stability of the closed loop system for linear time invariant systems with delays in the states. We show that conditions for the existence of a solution to this problem (the so-called regulation problem), similar to those known for the case of delay-free linear systems, may be given. We propose a solution for both the state and error feedback regulation.
This paper deals with the problem of tracking a reference signal while maintaining the stability of the closed loop system for linear time invariant systems with delays in the states. We show that conditions for the existence of a solution to this problem (the so-called regulation problem), similar to those known for the case of delay-free linear systems, may be given. We propose a solution for both the state and error feedback regulation.
Classification : 93B52, 93C05, 93C23
Keywords: linear systems; regulator theory; delay systems 
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     author = {Castillo-Toledo, Bernardino and N\'u\~nez-P\'erez, Eduardo},
     title = {On the regulator problem for a class of {LTI} systems with delays},
     journal = {Kybernetika},
     pages = {415--432},
     year = {2003},
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     zbl = {1249.93087},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2003_39_4_a1/}
}
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Castillo-Toledo, Bernardino; Núñez-Pérez, Eduardo. On the regulator problem for a class of LTI systems with delays. Kybernetika, Tome 39 (2003) no. 4, pp. 415-432. http://geodesic.mathdoc.fr/item/KYB_2003_39_4_a1/

[1] Alekal Y., Brunovský P., Chyung D. H., Lee E. B.: The quadratic problem for systems with time delays. IEEE Trans. Automat. Control 16 (1971), 673–687 | DOI | MR

[2] Boyd S., Ghaoui L. El, Feron, E., Balakrisnan V.: Linear Matrix Inequalities in System and Control Theory. SIAM Stud. Appl. Math., Philadelphia 1994 | MR

[3] Chyung D. H.: Tracking controller for linear systems with time delays in both state and control variables. J. of Dyn. Syst. Meas. and Control 115 (1993), 179–183 | DOI | Zbl

[4] Francis B. A.: The linear multivariable regulator problem. SIAM J. Control Optim. 15 (1977), 486–505 | DOI | MR

[5] Hale J. K., Verduyn-Lunel S. M.: Introduction to Functional Differential Equations. Springer–Verlag, New York 1993 | MR | Zbl

[6] Hautus B. M.: Linear matrix equations with applications to the regulator problem. In: Outils et Modèles Math ématiques pour l’Automatique l’Analyse de Sistèmes et le Traitement du Signal (I. D. Landau, ed.), CNRS, Paris 1983, pp. 399–412 | MR

[7] Hautus M. L. J.: On the Solvability of Linear Matrix Equations. Memorandum 1982-072, 1988

[8] Isidori A., Byrnes C. I.: Output regulation of nonlinear systems. IEEE Trans. Automat. Control 35 (1990), 131–140 | DOI | MR | Zbl

[9] Kamen E. W., Khargonekar P. P., Tannembaum A.: Stabilization of time-delay systems using finite-dimensional compensators. Trans. Automat. Control 30 (1985), 75–78 | DOI | MR

[10] Ni M. L., Er M. J., Leithead W. E., Leith D. J.: New approach to the design of robust tracking and model following controllers for uncertain delay systems. Proc. IEE–D, Control Theory Appl. 148 (2001), 6, 472–477

[11] Soliman M. A., Ray W. H.: Optimal control of multivariable systems with pure time delays. Automatica 7 (1971), 681–689 | DOI | Zbl

[12] Watanabe K., Nobuyama E., Kitamori, T., Ito M.: A new algorithm for finite spectrum assignment of single-input systems with time delay. IEEE Trans. Automat. Control 37 (1992), 1377–1383 | DOI | MR | Zbl

[13] Wonham W. M.: Linear Multivariable Control: A Geometric Approach. Springer–Verlag, New York 1979 | MR | Zbl

[14] Yen N. Z., Wu Y. C.: Multirate robust servomechanism controllers of linear delay systems using a hybrid structure. Internat. J. Control 60 (1994), 1265–1281 | DOI | MR | Zbl

[15] Zavarei M., Jamshidi M.: Time Delay Systems. Analysis, Optimization and Applications (North–Holland Systems and Control Series). North Holland, Amsterdam 1987 | MR | Zbl