The cluster treatment of characteristic roots and the neutral type time-delayed systems

Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME

Volumn 127, Issue 1, 2005, Pages 88-97

  Olgac, Nejat ^a   Sipahi, Rifat ^a  

^a UNIVERSITY OF CONNECTICUT   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CLUSTER TREATMENT; LINEAR TIME INVARIANT-NTDS (LTI-NTDS); NEUTRAL TIME-DELAYED SYSTEMS (NTDS); RETARDED TIME DELAY SYSTEMS (RTDS);

BYPRODUCTS; FUNCTIONS; MATHEMATICAL MODELS; MATRIX ALGEBRA; POLYNOMIALS; ROOT LOCI; SET THEORY; SYSTEM STABILITY;

DELAY CIRCUITS;

EID: 20144380083     PISSN: 00220434     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.1876494     Document Type: Article

References (27)

1. Barnett, S., 1983, Polynomials and Linear Control Systems, Marcel Dekker, New York.
2. Bellman, R., and Cooke, K., 1963, Differential Difference Equations, Academic, New York.
3. Chen, J., 1995, "On Computing the Maximal Delay Intervals for Stability of Linear Delay Systems," IEEE Trans. Autom. Control, 40, pp. 1087-1092.
4. Cooke, K. L., and van den Driessche, P., 1986, "On Zeroes of Some Transcendental Equations," Funkcialaj Ekvacioj, 29, pp. 77-90.
5. Halanay, A., 1966, Differential Equations: Stability, Oscillations, Time Lags, Academic, New York.
6. Hale, J. K., 1977, Theory of Functional Differential Equations, Springer-Verlag, New York.
7. Hale, J. K., 2001, "Stability, Control and Small Delays," 3rd IFAC TDS Workshop, New Mexico.
8. Hale, J. K., and Verduyn Lunel, S. M., 1993, An Introduction to Functional Differential Equations, Springer-Verlag, New York.
9. Hale, J. K., and Verduyn Lunel, S. M., 2001, "Effects of Small Delays on Stability and Control," Operator Theory; Advances and Applications, 122, pp. 275-301.
10. Hale, J. K., and Verduyn Lunel, S. M., 2001, "Strong Stabilization of Neutral Functional Differential Equations," IMA J. Math. Control Inform., 19, pp. 1-19.
11. Hale, I. K., Infante, E. F., and Tsen, F. S. P., 1985, "Stability in Linear Delay Equations," J. Math. Anal. Appl., 105, pp. 533-555.
12. Hertz, D., Jury, E. I., and Zeheb, E., 1984, "Simplified Analytic Stability Test for Systems with Commensurate Time Delays," IEE Proceedings, 131, Part D, No. 1, pp. 52-56.
13. Hu, Guang-Di, and Hu, Guang-Da, 1996, "Some Simple Criteria for Stability of Neutral Delay-Differential Systems," Appl. Math. Comput., 80, pp. 257-271.
14. Niculescu, S.-I., 2001, Delay Effects on Stability, Springer-Verlag, Berlin.
15. Olgac, N., and Sipahi, R., 2002, "An exact method for the stability analysis of time delayed LTI systems," IEEE Trans. Autom. Control, 47(5), pp. 793-797.
16. Kuo, B. C., 1991, Automatic Control Systems, Prentice-Hall, New Jersey.
17. Sipahi, R., and Olgac, N., 2003, "A New Perspective for Time Delayed Control Systems with Application to Vibration Suppression," ASME J. Vibr. Acoust., 125, pp. 384-388.
18. Sipahi, R., and Olgac, N., 2003, "Degenerate Cases in Using the Direct Method," ASME J. Dyn. Syst., Meas., Control, 125, pp. 194-201.
19. Marshall, J. E., 1979, Control of Time-Delay Systems, The Institute of Electrical Engineers, London and New York, Peter Peregrinus Ltd., Stevenage, UK and New York.
20. Park, P., 1999, "A Delay-Dependent Stability Criterion for Systems with Uncertain Time-Invariant Delays," IEEE Trans. Autom. Control, 44, pp. 876-877.
21. Rekasius, Z. V., 1980, "A Stability Test for Systems with Delays," in Proceedings of the Joint Automatic Control Conference, Paper No. TP9-A.
22. Thowsen, A., 1981, "The Routh-Hurwitz Method for Stability Determination of Linear Differential-Difference Systems," Int. J. Control, 33(5), pp. 991-995.
23. Thowsen, A., 1981, "An Analytic Stability Test for a Class of Time-Delay Systems," IEEE Trans. Autom. Control, 26(3), pp. 735-736.
24. Olgac, N., and Sipahi, R., May 2004, "Direct Method For Analyzing The Stability Of Neutral Type LTI-Time Delayed Systems," Automatica, 40(5), pp. 847-853.
25. Wells, D., 1986, The Penguin Dictionary of Curious and Interesting Numbers, Penguin Books, Middlesex, pp. 61-67.
26. Kolmanovski, V. B., and Nosov, V. R., 1986, Stability of Functional Differential Equations, Academic, London.
27. Mathews, J. H., and Howell, R. W., 1996, Complex Analysis for Mathematics and Engineering, Wm. C. Brown.