On stability of linear time-delay systems with multiple delays

International Journal of Systems Science

Volumn 39, Issue 8, 2008, Pages 839-852

  Park, Gwang Seok ^a   Choi, Ho Lim ^b   Lim, Jong Tae ^a  

^a Korea Advanced Institute of Science and Technology (KAIST)   (South Korea)

^b Dong A University   (South Korea)

Author keywords

Integral inequality; LMI; N segmentation of delay length; Time delay system

Indexed keywords

DELAY CONTROL SYSTEMS; EIGENVALUES AND EIGENFUNCTIONS; STABILITY CRITERIA; SYSTEM STABILITY; TIME DELAY;

DELAY BOUNDS; DELAY DEPENDENT STABILITY; INTEGRAL INEQUALITIES; LINEAR TIME-DELAY SYSTEMS; LYAPUNOV-KRASOVSKII FUNCTIONAL APPROACH; MULTIPLE DELAYS; NEUTRAL SYSTEMS; SIMULATION RESULTS; STABILITY BOUNDARIES;

ASYMPTOTIC STABILITY;

EID: 46149106177     PISSN: 00207721     EISSN: 14645319     Source Type: Journal    
DOI: 10.1080/00207720801903133     Document Type: Article

References (33)

1. Brierley, S.D., Chiasson, J.N., and Zak, S.H. (1982), "On stability independent of delay for linear systems," IEEE Transactions on Automatic Control, 27, 252-254.
2. Fridman, E. (2001), "New Lyapunov-Krasovskii functionals for stability of linear retared and neutral type systems," Systems and Control Letters, 43, 309-319.
3. Fridman, E., and Shaked, U. (2002), "An improved stabilization method for linear time-delay systems," IEEE Transactions on Automatic Control, 47, 1931-1937.
4. infin; control: constant and time-varying delays," International Journal of Control, 76, 48-60.
5. Fridman, E. (2006), "Descriptor discretised Lyapunov functional method: analysis and design," IEEE Transactions on Automatic Control, 51, 890-897.
6. Gahinet, P., Nemirovski, A., Laub, A.J., and Chilali, M. (1995), LMI Control Toolbox for Use with MATLAB, Natick, MA: MathWorks.
7. Gouaisbaut, F., and Peaucelle, D. (2006a), "Delay-dependent robust stability of time delay systems," Preprints of IFAC Symposium on Robust Control Design, Toulouse: France.
8. Gouaisbaut, F., and Peaucelle, D. (2006b), "Delay-dependent robust stability of time delay system," Preprints of IFAC Workshop on Time Delay Systems, L'Aquila: Italy.
9. Gu, K. (1997), "Discretized LMI set in the stability problem of linear uncertain time-delay systems," International Journal of Control, 68, 923-934.
10. Hale, J.K., and Lunel, S.M.V. (1993), Introduction to Functional Differential Equations, New York: Springer.
11. Han, Q.L., and Gu, K. (2001), "On robust stability of time-delay systems with norm-bounded uncertainty," IEEE Transactions on Automatic Control, 46, 1426-1431.
12. Han, Q.L., Gu, K., and Yu, X. (2003), "An improved estimate of the robust stability bound of time-delay systems with norm-bounded uncertainty," IEEE Transactions on Automatic Control, 48, 1629-1634.
13. Han, Q.L. (2005), "On stability of linear neutral systems with mixed time delays: a discretised Lyapunov functional approach," Automatica, 41, 1209-1218.
14. He, Y., Wu, M., She, J.H., and Liu, G.P. (2004), "Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays," Systems and Control Letters, 51, 57-65.
15. Kolmanovskii, V.B., and Nosov, V.R. (1986), Stability of Functional Differential Equations, New York: Academic.
16. Kolmanovskii, V.B., and Richard, J.P. (1999), "Stability of some linear systems with delays," IEEE Transactions on Automatic Control, 44, 984-989.
17. Lewis, R.M., and Anderson, B.D.O. (1980), "Necessary and sufficient conditions for delay-independent stability of linear autonomous system," IEEE Transactions on Automatic Control, 25, 735-739.
18. Li, X., and Souza, C.E.D. (1997), "Delay-dependent robust stability and stabilization of uncertain linear delay systems: a linear matrix inequality approach," IEEE Transactions on Automatic Control, 42, 1144-1148.
19. Moon, Y.S., Park, P.G., Kwon, W.H., and Lee, Y.S. (2001), "Delay-dependent robust stabilization of uncertain state-delayed systems," International Journal of Control, 74, 1447-1455.
20. Mori, T., Fukuma, N., and Kuwahara, M. (1981), "Simple stability criteria for single and composite linear systems with time delay," International Journal of Control, 34, 1175-1184.
21. Mori, T., Fukuma, N., and Kuwahara, M. (1982), "On an estimation of decay rate for stable linear delay systems," International Journal of Control, 36, 95-97.
22. Mori, T., and Kokame, H. (1989), "Stability of ẋ(t) = Ax(t) + Bx(t - τ)," IEEE Transactions on Automatic Control, 34, 460-462.
23. Niculescu, S.I., Neto, A.T., Dion, J.M., and Dugard, L., (1995), "Delay-dependent stability of linear systems with delayed state: an LMI approach", in Proceedings of 34th Conference on Decision and Control, LA, USA, New Orleans, 1495-1496.
24. Niculescu, S.I., (1999), "A model transformation class for delay-dependent stability analysis", in Proceedings of the America Control Conference, San Diego, California, 314-318.
25. Park, P.G. (1999), "A delay-dependent stability criterion for systems with uncertain time-invariant delays," IEEE Transactions on Automatic Control, 44, 876-877.
26. Peaucelle, D., Henrion, D., and Arzelier, D. (2005), "Quadratic separation for feedback connection of an uncertain matrix and an implicit linear transformation," Preprints of the 16th IFAC World Congress, Prague: Czech Republic.
27. Richard, J.P. (2003), "Time-delay systems: an overview of some recent advances and open problems," Automatica, 39, 1667-1694.
28. Sipahi, R., and Olgac, N. (2005), "Complete stability robustness of third-order LTI multiple time-delay system," Automatica, 41, 1413-1422.
29. Su, J.H., Fung, I.K., and Tseng, C.L. (1994), "Stability analysis linear systems with time delay," IEEE Transactions on Automatic Control, 39, 1341-1344.
30. Suh, I.H., and Bien, Z. (1982), "A note on the stability of large scale systems with delays," IEEE Transactions on Automatic Control, 27, 256-258.
31. Vyhlidal, T., and Zitek, P. (2006), "Analysis of infinite spectra of time delay systems using quasipolynomial root finder implemented in MATLAB," Preprints of IFAC Workshop on Time Delay Systems, L'Aquila: Italy.
32. Wu, M., He, Y., She, J.H., and Liu, G.P. (2004), "Delay-dependent criteria for robust stability of time-varying delay systems," Automatica, 40, 1435-1439.
33. Xu, B. (1995), "On delay-independent stability of large-scale systems with time delays," IEEE Transactions on Automatic Control, 40, 930-933.