Article
Full entry |
PDF
(2.6 MB)
Feedback
PDF
(2.6 MB)
Feedback
Keywords:
linear systems; regulator theory; delay systems
linear systems; regulator theory; delay systems
Summary:
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.
References:
[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 10.1109/TAC.1971.1099824 | MR 0308892
[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 1284712
[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 10.1115/1.2897394 | Zbl 0776.93056
[4] Francis B. A.: The linear multivariable regulator problem. SIAM J. Control Optim. 15 (1977), 486–505 DOI 10.1137/0315033 | MR 0446631
[5] Hale J. K., Verduyn-Lunel S. M.: Introduction to Functional Differential Equations. Springer–Verlag, New York 1993 MR 1243878 | Zbl 0787.34002
[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 0783851
[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 10.1109/9.45168 | MR 1038409 | Zbl 0704.93034
[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 10.1109/TAC.1985.1103789 | MR 0777079
[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 10.1016/0005-1098(71)90006-9 | Zbl 0242.49025
[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 10.1109/9.159575 | MR 1183097 | Zbl 0755.93022
[13] Wonham W. M.: Linear Multivariable Control: A Geometric Approach. Springer–Verlag, New York 1979 MR 0569358 | Zbl 0609.93001
[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 10.1080/00207179408921520 | MR 1305036 | Zbl 0825.93220
[15] Zavarei M., Jamshidi M.: Time Delay Systems. Analysis, Optimization and Applications (North–Holland Systems and Control Series). North Holland, Amsterdam 1987 MR 0930450 | Zbl 0658.93001
Search
Partner of
