Kernel and offspring concepts for the stability robustness of Multiple Time Delayed Systems (MTDS)

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

Volumn 129, Issue 3, 2007, Pages 245-251

  Sipahi, Rifat ^a,b   Olgac, Nejat ^b  

^a Northeastern University   (United States)

^b UNIVERSITY OF CONNECTICUT   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

LINEAR TIME INVARIANT (LTI) SYSTEMS; MULTIPLE TIME DELAYED SYSTEMS (MTDS);

ROBUSTNESS (CONTROL SYSTEMS); TIME DELAY;

SYSTEM STABILITY;

EID: 34250811909     PISSN: 00220434     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2718235     Document Type: Article

References (23)

1. Hsu, C. S., and Bhatt, K. L., 1996, "Stability Charts for Second-Order Dynamical Systems With Time Lag," J. Appl. Mech., 33, pp. 119-124.
2. Rekasius, Z. V., 1980, "A Stability Test for Systems With Delays," presented at Proceedings of the Joint Automatic Control Conference, Paper No. TP9-A.
3. Hsu, C. S., 1970, "Application of the Tau-Decomposition Method to Dynamical Systems Subjected to Retarded Follower Forces," ASME J. Appl. Mech., 37, pp. 258-266.
4. Cooke, K. L., and van den Driessche, P., 1986, "On Zeros of Some Transcendental Equations," Funkc. Ekvac., 29, pp. 77-90.
5. Chen, J., Gu, G., and Nett, C. N., 1995, "A New Method for Computing Delay Margins for Stability of Linear Delay Systems," Syst. Control Lett., 26, pp. 107-117.
6. Bellman, R. E., and Cooke, K. L., 1963, Differential-Difference Equations, Academic, New York.
7. Olgac, N., and Sipahi, R., 2002, "An Exact Method for the Stability Analysis of Time Delayed Lti Systems," IEEE Trans. Autom. Control, 47, pp. 793-797.
8. Sipahi, R., and Olgac, N., 2006, "A Novel Stability Study on Multiple Time-Delay Systems Using the Root Clustering Paradigm," Syst. Control Lett., 55, pp. 819-825.
9. Sipahi, R., and Olgac, N., 2003, "Degenerate Cases in Using Direct Method," ASME J. Dyn. Syst., Meas., Control, 125, pp. 194-201.
10. Sipahi, R., and Olgac, N., 2003, "Active Vibration Suppression With Time Delayed Feedback," ASME J. Vibr. Acoust., 125, pp. 384-388.
11. Niculescu, S.-I., 2002, "On Delay Robustness Analysis of a Simple Control Algorithm in High-Speed Networks," Automatica, 38, pp. 885-889.
12. Stepan, G., 1989, Retarded Dynamical Systems: Stability and Characteristic Function, Longman Scientific & Technical and Wiley, New York.
13. MacDonald, N., 1987, "An Interference Effect of Independent Delays," Proc. IEEE, 134, pp. 38-42.
14. Hale, J. K., and Huang, W., 1993, "Global Geometry of the Stable Regions for Two Delay Differential Equations," J. Math. Anal. Appl., 178, pp. 344-362.
15. Breda, D., Maset, S., and Vermiglio, R., 2004, "Computing the Characteristic Roots for Delay Differential Equations," IMA J. Numer. Anal., 24, pp. 1-19.
16. Rekasius, Z. V., 1980, "A Stability Test for Systems With Delays," presented at Proceedings of the Joint Automatic Control Conference, TP9-A, San Francisco, CA.
17. Thowsen, A., 1981, "The Routh-Hurwitz Method for Stability Determination of Linear Differential-Difference Systems," Int. J. Control, 33, pp. 991-995.
18. Hertz, D., Jury, E. I., and Zeheb, E., 1984, "Simplified Analytic Stability Test for Systems With Commensurate Time Delays," IEE Proc.-D: Control Theory Appl., 131, pp. 52-56.
19. Ogata, K., 2004, System Dynamics, 4th ed., Pearson-Prentice Hall, New York.
20. Hale, J. K., and Verduyn Lunel, S. M., 2001, "Strong Stabilization of Neutral Functional Differential Equations," IMA J. Math. Control Inf., 19, pp. 1-19.
21. Hale, J. K., and Verduyn Lunel, S. M., 2001, "Effects of Small Delays on Stability and Control," Operator Theory and Analysis; Advances and Applications, Birkhauser, 122, pp. 275-301.
22. Kolmanovskii, V. B., and Nosov, V. R., 1989 Stability of Functional Differential Equations, Academic, London.
23. Sipahi, R., and Olgac, N., 2005, "Complete Stability Robustness of Third Order, LTI, Multiple Time-Delay Systems," Automatica, 41, pp. 1413-1422.