Geodesic
Meromorphic observer-based pole assignment in time delay systems
Kybernetika, Tome 44 (2008) no. 5, pp. 633-648 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

The paper deals with a novel method of control system design which applies meromorphic transfer functions as models for retarded linear time delay systems. After introducing an auxiliary state model a finite-spectrum observer is designed to close a stabilizing state feedback. The observer finite spectrum is the key to implement a state feedback stabilization scheme and to apply the affine parametrization in controller design. On the basis of the so- called RQ-meromorphic functions an algebraic solution to the problem of time- delay system stabilization and control is presented that practically provides a finite spectrum assignment of the control loop.
The paper deals with a novel method of control system design which applies meromorphic transfer functions as models for retarded linear time delay systems. After introducing an auxiliary state model a finite-spectrum observer is designed to close a stabilizing state feedback. The observer finite spectrum is the key to implement a state feedback stabilization scheme and to apply the affine parametrization in controller design. On the basis of the so- called RQ-meromorphic functions an algebraic solution to the problem of time- delay system stabilization and control is presented that practically provides a finite spectrum assignment of the control loop.
Classification : 93B55, 93C05, 93D15
Keywords: retarded time-delay system; meromorphic transfer function; reduced-order observer; state feedback; affine parametrization of stabilizing controllers 
@article{KYB_2008_44_5_a2,
     author = {Z{\'\i}tek, Pavel and Ku\v{c}era, Vladim{\'\i}r and Vyhl{\'\i}dal, Tom\'a\v{s}},
     title = {Meromorphic observer-based pole assignment in time delay systems},
     journal = {Kybernetika},
     pages = {633--648},
     year = {2008},
     volume = {44},
     number = {5},
     mrnumber = {2479309},
     zbl = {1177.93043},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2008_44_5_a2/}
}
TY  - JOUR
AU  - Zítek, Pavel
AU  - Kučera, Vladimír
AU  - Vyhlídal, Tomáš
TI  - Meromorphic observer-based pole assignment in time delay systems
JO  - Kybernetika
PY  - 2008
SP  - 633
EP  - 648
VL  - 44
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/KYB_2008_44_5_a2/
LA  - en
ID  - KYB_2008_44_5_a2
ER  - 
%0 Journal Article
%A Zítek, Pavel
%A Kučera, Vladimír
%A Vyhlídal, Tomáš
%T Meromorphic observer-based pole assignment in time delay systems
%J Kybernetika
%D 2008
%P 633-648
%V 44
%N 5
%U http://geodesic.mathdoc.fr/item/KYB_2008_44_5_a2/
%G en
%F KYB_2008_44_5_a2
Zítek, Pavel; Kučera, Vladimír; Vyhlídal, Tomáš. Meromorphic observer-based pole assignment in time delay systems. Kybernetika, Tome 44 (2008) no. 5, pp. 633-648. http://geodesic.mathdoc.fr/item/KYB_2008_44_5_a2/

[1] Breda D., Maset S., Vermiglio R.: Computing the characteristic roots for delay differential equations. IMA J. Numer. Anal. 24 (2004), 1, 1–19 | MR | Zbl

[2] Hale J. K., Lunel S. M. Verduyn: Introduction to Functional Differential Equations (Mathematical Sciences Vol. 99). Springer-Verlag, New York 1993 | MR

[3] Goodwin G. C., Graebe S. F., Salgado M. E.: Control System Design. Prentice Hall, Englewood Cliffs, N.J. 2001

[4] Kim J. H., Park H. B.: State feedback control for generalized continuous/discrete time-delay systems. Automatica 35 (1999), 8, 1443–1451 | MR

[5] Loiseau J. J.: Algebraic tools for the control and stabilization of time-delay systems. Ann. Review in Control 24 (2000), 135–149

[6] Michiels W., Engelborghs K., Vansevenant, P., Roose D.: Continuous pole placement method for delay equations. Automatica 38 (2002), 5, 747–761 | MR

[7] Michiels W., Roose D.: Limitations of delayed state feedback: a numerical study. Internat. J. Bifurcation and Chaos 12 (2002), 6, 1309–1320

[8] Michiels W., Vyhlídal T.: An eigenvalue based approach for the stabilization of linear time-delay systems of neutral type. Automatica 41 (2005), 991–998 | MR | Zbl

[9] Mirkin L., Raskin N.: Every stabilizing dead-time controller has an observer-predictor-based structure. Automatica 39 (2003), 1747–1754 | MR | Zbl

[10] Niculescu S. I., (eds.) K. Gu: Advances in Time-Delay Systems. Springer-Verlag, Berlin – Heidelberg 2004 | MR | Zbl

[11] Olbrot W.: Stabilizability, detectability and spectrum assignment for linear autonomous systems with general time delays. IEEE Trans. Automat. Control 23 (1978), 5, 887–890 | MR | Zbl

[12] Picard P., Lafay J. F., Kučera V.: Feedback realization of non-singular precompensators for linear systems with delays. IEEE Trans. Automat. Control 42 (1997), 6, 848–853 | MR

[13] Trinh H.: Linear functional state observer for time delay systems. Internat. J. Control 72 (1999), 18, 1642–1658 | MR | Zbl

[14] Vyhlídal T., Zítek P.: Mapping the spectrum of a retarded time-delay system utilizing root distribution features. In: Proc. IFAC Workshop on Time-Delay Systems, TDS’06, L’Aquila 2006

[15] Vyhlídal T., Zítek P.: Mapping based algorithm for large-scale computation of quasi-polynomial zeros. IEEE Trans. Automat. Control (to appear) | MR

[16] Wang Q. E., Lee T. H., Tan K. K.: Finite Spectrum Assignment Controllers for Time Delay Systems. Springer, London 1995

[17] Zhang W., Algower, F., Liu T.: Controller parametrization for SISO and MIMO plants with time-delay. Systems Control Lett. 55 (2006), 794–802 | MR

[18] Zítek P., Hlava J.: Anisochronic internal model control of time delay systems. Control Engrg. Practice 9 (2001), 5, 501–516

[19] Zítek P., Kučera V.: Algebraic design of anisochronic controllers for time delay systems. Internat. J. Control 76 (2003), 16, 1654–1665 | MR

[20] Zítek P., Vyhlídal T.: Quasi-polynomial based design of time delay control systems. In: Fourth IFAC Workshop on Time Delay Systems, Rocquencourt 2003