Robust stability of quasi-polynomials: Frequency-sweeping conditions and vertex tests

IEEE Transactions on Automatic Control

Volumn 53, Issue 5, 2008, Pages 1219-1234

  Chen, Jie ^a   Niculescu, Silviu Iulian ^c   Fu, Peilin ^a,b  

^a University of California Riverside   (United States)

^b NATIONAL UNIVERSITY   (United States)

^c CNRS   (France)

Author keywords

Frequency sweeping tests; Robust stability; Timedelay systems; Uncertain quasi polynomials; Vertex tests

Indexed keywords

CONTROL THEORY; DELAY CONTROL SYSTEMS; DIAMONDS; OPTICAL BISTABILITY; POLYNOMIAL APPROXIMATION; ROBUSTNESS (CONTROL SYSTEMS); SYSTEM STABILITY; TIME DELAY; TRAJECTORIES;

FREQUENCY-DEPENDENT; FREQUENCY-SWEEPING TESTS; NECESSARY AND SUFFICIENT CONDITIONS; QUASI-POLY-NOMIAL; QUASI-POLYNOMIALS; ROBUST STABILITY; ROBUST STABILITY ANALYSIS; ROBUSTLY STABLE; STABILITY INDEPENDENT OF DELAY; TIMEDELAY SYSTEMS; UNCERTAIN QUASI-POLYNOMIALS; UNCERTAIN TIME-DELAY SYSTEMS; VERTEX TESTS;

POLYNOMIALS;

EID: 51849126554     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2008.923686     Document Type: Article

References (33)

1. B. R. Barmish, New Tools for Robustness of Linear Systems. New York, NY: Macmillan, 1994.
2. A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences. New York: Academic, 1979.
3. S. P. Bhattacharyya, H. Chapellat, and L. H. Keel, Robust Control. The Parametric Approach. Upper Saddle River, NJ: Prentice Hall, 1995.
4. P. A. Bliman, "Lyapunov equation for the stability of linear delay systems of retarded and neutral type," IEEE Trans. Autom. Control vol. 47, no. 2, pp. 327-335, Feb. 2002.
5. P. A. Bliman, "Nonconservative LMI approach to robust stability for systems with uncertain scalar parameters," in Proc. 41st IEEE Conf. Decision Contr., Las Vegas, NV, Dec. 2002, pp. 305-310.
6. J. Chen, "On computing the maximal delay intervals for stability of linear delay systems," IEEE Trans. Autom. Control, vol. 40, pp. 1087-1093, 1995.
7. J. Chen and H. A. Latchman, "Frequency sweeping tests for stability independent of delay," IEEE Trans. Autom. Control, vol. 40, pp. 1640-1645, 1995.
8. J. Chen, M. K. H. Fan, and C. N. Nett, "Structured singular values and stability analysis of uncertain polynomials, part 1: The generalized μ," Syst. Contr. Lett., vol. 23, pp. 53-65, 1994.
9. J. Chen, M. K. H. Fan, and C. N. Nett, "Structured singular values and stability analysis of uncertain polynomials, part 2: A missing link," Syst. Contr. Lett., vol. 23, pp. 97-109, 1994.
10. J. Chen, G. Gu, and C. N. Nett, "A new method for computing delay margins for stability of linear delay systems,," Syst. Contr. Lett. vol. 26, pp. 101-117, 1995.
11. J. Chen and S. I. Niculescu, "Robust stability of quasi-polynomials: Frequency-sweeping conditions," in Proc. 42nd IEEE Conf. Dec. Contr. Maui, HI, Dec. 2003, pp. 5048-5053.
12. J. Chen and S. I. Niculescu, "Robust stability of quasi-polynomials: Vertex tests and extensions," in Proc. 2004 Amer. Contr. Conf., Boston, MA, Jun. 2004, pp. 4159-4164.
13. J. Chen and A. L. Tits, "Robust control analysis," in Encyclopedia of Electrical and Electronics Engineering, J. G. Webster, Ed. New York: Wiley, 1998, vol. 18, pp. 602-616.
14. M. Fu, A. W. Olbrot, and M. P. Polis, "Robust stability for time-delay systems: The edge theorem and graphical tests," IEEE Trans. Autom. Control, vol. 34, pp. 813-820, 1989.
15. G. H. Golub and C. F. Van Loan, Matrix Computations. Baltimore, MD: Johns Hopkins Univ. Press, 1985.
16. K. Gu, V. L. Kharitonov, and J. Chen, Stability and Robust Stability of Time-Delay Systems. Boston, MA: Birkhauser, 2003.
17. J. K. Hale and S. M. Verduyn Lunel, "Introduction to functional differential equations," in Applied Math. Sciences. New York: Springer-Verlag, 1993, vol. 99.
18. J. K. Hale, E. F. Infante, and F. S. P. Tsen, "Stability in linear delay equations," J. Math. Anal. Appl., vol. 105, pp. 533-555, 1985.
19. J. Hocherman, V. L. Kharitonov, J. Kogan, and E. Zeheb, "On the stability of quasi-polynomials with weighted diamond coefficients," Multidimensional Syst. Sig. Proc., vol. 5, pp. 397-418, 1994.
20. R. A. Horn, "The Hadamard product," in Proc. Symp. Appl. Math., 1980, vol. 40, pp. 87-169.
21. V. L. Kharitonov and L. Atanassova, "On stability of wheighted diamond of real quasi-polynomials," IEEE Trans. Autom. Control, vol. 42, pp. 831-835, 1997.
22. V. L. Kharitonov and R. Tempo, "On the stability of a weighted diamond of real polynomials," Syst. Contr. Lett., vol. 22, no. 1, pp. 5-7, Jan. 1994. 23 V. L. Kharitonov and A. Zhabko, "Robust stability of time delay systems," IEEE Trans. Autom. Control, vol. 39, pp. 2388-2397, 1994.
23. K. D. Kim and N. K. Bose, "Vertex implications of stability for a class of delay-differential interval systems," IEEE Trans. Circuits Syst. vol. 37, no. 7, pp. 969-972, Jul. 1990.
24. J. Kogan, Robust Stability and Convexity: An Introduction, ser. Lecture Notes in Control Information Science. New York: Springer-Verlag, 1995.
25. J. Kogan and A. Leizarowitz, "Frequency domain criterion for robust stability of interval time-delay systems," Automatica, vol. 31, no. 3, pp. 463-469, Mar. 1995.
26. J. Kogan and A. Leizarowitz, "Exponential stability of linear systems with commensurate time-delays," Math. Contr. Sig. Syst., vol. 8, pp. 65-81, 1995.
27. V. B. Kolmanovskii and V. R. Nosov, Stability of Functional Differential Equations. New York: Academic, 1986.
28. Y. Li, K. M. Nagpal, and E. Bruce Lee, "Stability analysis of polynomials with coefficients in disks," IEEE Trans. Autom. Control vol. 37, pp. 509-513, 1992.
29. M. S. Mahmoud, Robust Control and Filtering for Time-Delay Systems New York: Marcel Dekker, 2000.
30. T. Mori and S. Barnett, "On stability tests for some classes of dynamical systems with perturbed coefficients," IMA J. Math. Contr. Inf., vol. 5, pp. 117-123, 1988.
31. S.-I. Niculescu, Delay Effects on Stability. A Robust Control Approach. Heidelberg, Germany: Springer-Verlag, 2001, vol. 269 LNCIS.
32. A. W. Olbrot and C. U. T. Igwe, "Necessary and sufficient conditions for rubust stability independent of delays and coefficient perturbations," in Proc. 34th IEEE Conf. Decision Contr., New Orleans, LA, Dec. 1995, pp. 392-394.
33. O. Toker and H. Ozbay, "Complexity issues in robust stability of linear delay-differential systems," Math., Contr., Signals, Syst., vol. 9, pp. 386-400, 1996.