Extraction of 3D stability switching hypersurfaces of a time delay system with multiple fixed delays

Automatica

Volumn 45, Issue 6, 2009, Pages 1449-1454

  Sipahi, Rifat ^a   Delice, Ismail Ilker ^a  

^a Northeastern University   (United States)

Author keywords

Hypersurfaces; Multiple fixed delays; Stability switching; Time delay systems

Indexed keywords

COMPUTATION TIME; D STABILITIES; GENERAL CLASS; HYPERSURFACES; LINEAR TIME INVARIANTS; MULTIPLE FIXED DELAYS; MULTIPLE TIME-DELAY SYSTEMS; NON-TRIVIAL; ORDER OF MAGNITUDES; STABILITY SWITCHING; TIME DELAY SYSTEMS;

INTERNET PROTOCOLS; SURFACES; SWITCHING; TIME DELAY;

SYSTEM STABILITY;

EID: 67349109817     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2009.01.017     Document Type: Article

References (26)

1. Bozorg M., and Davison E.J. Control of time delay processes with uncertain delays: Time delay stability margins. Journal of Process Control 16 4 (2006) 403-408
2. Chen J., and Latchman H.A. Frequency sweeping tests for asymptotic stability independent of delay. IEEE Transactions on Automatic Control 40 9 (1995) 1640-1645
3. Chen J., Niculescu S.-I., and Fu P. Robust stability of quasi-polynomials: Frequency-sweeping conditions and vertex tests. IEEE Transactions on Automatic Control 53 5 (2008) 1219-1234
4. Cooke K.L., and van den Driessche P. On zeros of some transcendental equations. Funkcialaj Ekvacioj 29 1 (1986) 77-90
5. Datko R. A procedure for determination of the exponential stability of certain differential-difference equations. Quarterly of Applied Mathematics 36 (1978) 279-292
6. Engelborghs, K. (2000). DDE-BIFTOOL: A Matlab package for bifurcation analysis of delay differential equations. TW Report 305. Department of Computer Science, Katholieke Universiteit Leuven, Belgium
7. Ergenc A.F., Olgac N., and Fazelinia H. Extended kronecker summation for cluster treatment of LTI systems with multiple delays. SIAM Journal on Control and Optimization 46 1 (2007) 143-155
8. Fazelinia H., Sipahi R., and Olgac N. Stability analysis of multiple time delayed systems using 'Building Block' concept. IEEE Transactions on Automatic Control 52 5 (2007) 799-810
9. Gu K., Kharitonov V.L., and Chen J. Stability of time-delay systems (2003), Birkhäuser, Boston
10. Gu K., Niculescu S.-I., and Chen J. On stability crossing curves for general systems with two delays. Journal of Mathematical Analysis and Applications 311 1 (2005) 231-253
11. Gündeş A.N., Özbay H., and Özgüler A. PID controller synthesis for a class of unstable MIMO plants with I/O delays. Automatica 43 1 (2007) 135-142
12. Hale J.K., and Lunel S.M.V. An introduction to functional differential equations. Applied mathematical sciences Vol. 99 (1993), Springer-Verlag, New York
13. Jarlebring E. Critical delays and polynomial eigenvalue problems. Journal of Computational and Applied Mathematics 224 1 (2009) 296-306
14. Kunz E. Introduction to plane algebraic curves (2005), Birkhäuser, Boston
15. Mazenc F., Mondié S., and Niculescu S.-I. Global asymptotic stabilization for chains of integrators with a delay in the input. IEEE Transactions on Automatic Control 48 1 (2003) 57-63
16. Michiels W., and Niculescu S.-I. Stability and stabilization of time-delay systems: An eigenvalue-based approach. Advances in design and control Vol. 12 (2007), SIAM, Philadelphia
17. Niculescu, S.-I., Kim, P. S., Gu, K., Lee, P. P., & Levy, D. (2009). Stability crossing boundaries of delay systems modeling immune dynamics in leukemia, (submitted for publication, private communication)
18. Niculescu S.-I., and Michiels W. Stabilizing a chain of integrators using multiple delays. IEEE Transactions on Automatic Control 49 5 (2004) 802-807
19. Ogata K. Modern control engineering (2002), Prentice-Hall, Upper Saddle River, NJ
20. Saberi A., Stoorvogel A.A., and Sannuti P. Control of linear systems with regulation and input constraints. Communication and control engineering (2000), Springer-Verlag, London, UK
21. Silva G.J., Datta A., and Bhattacharyya S.P. PI stabilization of first-order systems with time delay. Automatica 37 12 (2001) 2025-2031
22. Sipahi, R. (2007). An efficient numerical approach for the stability analysis of a class of LTI systems with arbitrary number of delays. In 7th IFAC workshop on time-delay systems
23. Sipahi R., and Olgac N. Complete stability robustness of third-order LTI multiple time-delay systems. Automatica 41 8 (2005) 1413-1422
24. Sipahi, R., & Olgac, N. (2006a). Stability map of systems with three independent delays. In Proceedings of the American control conference
25. Sipahi R., and Olgac N. Stability robustness of retarded LTI systems with single delay and exhaustive determination of their imaginary spectra. SIAM Journal on Control and Optimization 45 5 (2006) 1680-1696
26. Stépán G. Retarded dynamical systems: Stability and characteristic functions. Pitman research notes in mathematics series Vol. 210 (1989), Longman Scientific & Technical, co-publisher John Wiley & Sons, Inc, New York