Generalization of cluster treatment of characteristic roots for robust stability of multiple time-delayed systems

International Journal of Robust and Nonlinear Control

Volumn 18, Issue 14, 2008, Pages 1430-1449

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

^a UNIVERSITY OF CONNECTICUT   (United States)

^b Northeastern University   (United States)

Author keywords

Building block; Cluster treatment of characteristic roots; Linear time invariant (LTI) systems; Multiple time delays; Stability robustness

Indexed keywords

BUILDINGS; CONFORMAL MAPPING;

BUILDING BLOCK; CLUSTER TREATMENT OF CHARACTERISTIC ROOTS; LINEAR TIME-INVARIANT (LTI) SYSTEMS; MULTIPLE TIME DELAYS; STABILITY ROBUSTNESS;

SYSTEM STABILITY;

EID: 53149146310     PISSN: 10498923     EISSN: 10991239     Source Type: Journal    
DOI: 10.1002/rnc.1290     Document Type: Article

References (25)

1. Hale JK. Theory of Functional Differential Equations. Springer: New York, 1977.
2. Hale JK, Verduyn Lunel SM. An Introduction to Functional Differential Equations. Springer: New York, 1993.
3. Cooke KL, van den Driessche P. On zeros of some transcendental equations. Funkcialaj Ekvacioj 1986; 29:77-90.
4. Nussbaum R. Differential Delay Equations with Two Time Lags. Memoirs of American Mathematical Society, vol. 205. American Mathematical Society: Providence, RI, 1978.
5. Kamen EW. Linear systems with commensurate time delays: stability and stabilization independent of delay. IEEE Transactions on Automatic Control 1982; 25:367-375.
6. Chapellat H, Bhattacharyya SP. A generalization of Kharitonov's theorem: robust stability of interval plants. IEEE Transactions on Automatic Control 1989; 34:306-311.
7. Fu M, Olbrot AW, Polis MP. Robust stability for time-delayed systems: the edge theorem and graphical tests. IEEE Transactions on Automatic Control 1989; 34:813-819.
8. Kharitonov VL, Zhabko AP. Robust stability of time-delay systems. IEEE Transactions on Automatic Control 1994; 39:2388-2397.
9. Kharitonov VL. Robust stability analysis of time delay systems: a survey. Annual Reviews in Control 1999; 23:185-196.
10. Richard JP. Time-delay systems: an overview of some recent advances and open problems. Automatica 2003; 39:1667-1694.
11. Silva GJ, Datta A, Bhattacharyya SP. PI stabilization of first-order systems with time delay. Automatica 2001; 37:2025-2031.
12. Toker O, Ozbay H. Complexity issues in robust stability of linear delay-differential systems. Mathematics of Control, Signals and Systems 1996; 9:386-400.
13. Stepan G. Retarded Dynamical Systems: Stability and Characteristic Function. Longman, Wiley: New York, U.S., 1989.
14. Hale JK, Huang W. Global geometry of the stable regions for two delay differential equations. Journal of Mathematical Analysis and Applications 1993; 178:344-362.
15. Campbell SA. Stability and bifurcation of a simple neural network with multiple time delays. Fields Institute Communications 1999; 21:65-79.
16. Sipahi R, Olgac N. A unique methodology for the stability robustness of multiple time delay systems. Systems and Control Letters 2006; 55:819-825.
17. Sipahi R, Olgac N. Complete stability robustness of third order LTI multiple time-delay systems. Automatica 2005; 41:1413-1422.
18. El'sgol'ts LE, Norkin SB. Introduction to the Theory and Application of Differential Equations with Deviating Arguments. Academic Press: New York, 1973.
19. Olgac N, Sipahi R. An exact method for the stability analysis of time delayed LTI systems. IEEE Transactions on Automatic Control 2002; 47:793-797.
20. Rekasius ZV. A stability test for systems with delays. Proceedings of Joint Automatic Control Conference, San Francisco, 1980; Paper No. TP9-A.
21. Thowsen A. The Routh-Hurwitz method for stability determination of linear differential-difference systems. International Journal of Control 1981; 33:991-995.
22. Hertz D, Jury EI, Zeheb E. Simplified analytic stability test for systems with commensurate time delays. Proceedings of Institution of Electrical Engineers, Part (D) 1984; 131:52-56.
23. Susskind L. The world as a hologram. Journal of Mathematical Physics 1995; 36:6377-6396.
24. Kuo BC. Automatic Control Systems. Prentice-Hall: Englewood Cliffs, NJ, 1987.
25. Brewer JW. Kronecker products and matrix calculus in system theory. IEEE Transactions on Circuits and Systems 1978; CAS-25:772-781.