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retarded time-delay system; meromorphic transfer function; reduced-order observer; state feedback; affine parametrization of stabilizing controllers
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.
[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 2027286 | Zbl 1054.65079
[2] Hale J. K., Lunel S. M. Verduyn: Introduction to Functional Differential Equations (Mathematical Sciences Vol. 99). Springer-Verlag, New York 1993 MR 1243878
[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 1831484
[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 2133350
[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 2157698 | Zbl 1091.93026
[9] Mirkin L., Raskin N.: Every stabilizing dead-time controller has an observer-predictor-based structure. Automatica 39 (2003), 1747–1754 MR 2141770 | Zbl 1039.93026
[10] Niculescu S. I., (eds.) K. Gu: Advances in Time-Delay Systems. Springer-Verlag, Berlin – Heidelberg 2004 MR 2092594 | Zbl 1051.34002
[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 0528786 | Zbl 0399.93008
[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 1455716
[13] Trinh H.: Linear functional state observer for time delay systems. Internat. J. Control 72 (1999), 18, 1642–1658 MR 1733875 | Zbl 0953.93012
[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 2478083
[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 2246741
[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 2019076
[20] Zítek P., Vyhlídal T.: Quasi-polynomial based design of time delay control systems. In: Fourth IFAC Workshop on Time Delay Systems, Rocquencourt 2003
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