Asymptotic behavior of imaginary zeros of linear systems with commensurate delays

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2006, Pages 1375-1380

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

^a University of California ^*  (United States)

^b UNIVERSITÉ DE TECHNOLOGIE DE COMPIÈGNE   (France)

Author keywords

Asymptotic behavior; Asymptotic stability; Critical zeros; Matrix pencil; Time delay

Indexed keywords

ASYMPTOTIC ANALYSIS; EIGENVALUES AND EIGENFUNCTIONS; PERTURBATION TECHNIQUES; POLYNOMIALS; SYSTEM STABILITY; TIME DELAY;

ASYMPTOTIC BEHAVIOR; CRITICAL ZEROS; MATRIX PENCILS; QUASIPOLYNOMIAL;

LINEAR SYSTEMS;

EID: 39649102780     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/cdc.2006.377014     Document Type: Conference Paper

References (17)

1. H. Baumgärtel, Analytic Perturbation Theory for Matrices and Operators, Birkhauser, Boston; 1985.
2. F.G. Boese, Stability with respect to the delay: On the paper of K.L. Cooke and P. van den Driessche, J. Math. Anal.Appl, vol. 228, 1998, pp 293-321.
3. J. Chen, C. Gu and C.N. Nett, A new method for computing delay margins for stability of linear delay systems, Syst. & Contr. Lett., vol. 26, 1995, pp 101-117.
4. K.L. Cooke and Z. Grossman, Discrete delay, distributed delay and stability switches, J. Math. Anal. Appl., vol. 86, 1982, pp 592-627.
5. K.L. Cooke and P. Van den Driessche, On zeroes of some transcendental equations, Funkcialaj Ekvacioj, vol. 29, 1986, pp 77-90.
6. A.S. Deif, Advanced Matrix Theory for Scientists and Engineers, Abacus Press, England; 1982.
7. P. Fu, S.I. Niculescu and J. Chen, Stability of linear neutral time-delay systems: exact conditions via matrix pencil solutions, IEEE Trans. Automat. Contr., vol. 51, no. 6, 2006, pp 1063-1069.
8. K. Gu, V.L. Kharitonov and J. Chen, Stability of Time-Delay Systems, Birkhauser, Boston; 2003.
9. D. Hertz, E.I. Jury and E. Zeheb, Simplified analytical stability test for systems with commensurate time delays, IEE Proc. Contr. Theory & Appl., Pt. D, 131, 1984, pp 52-56.
10. T. Kailath, Linear Systems, Prentice-Hall, Englewood Cliffs, NJ; 1980.
11. T. Kato, Perturbation Theory for Linear Operations, Springer-Verlag, Berlin; 1995.
12. P. Lancaster, A.S. Markus and F. Zhou, Perturbation theory for analytic matrix functions: the semisimple case, SIAM J. Matrix Anal. Appl., vol. 25, no. 3, 2003, pp 606-626.
13. M.S. Lee and C.S. Hsu, On the r-decomposition method of stability analysis for retarded dynamic systems, SIAM J. Control, vol. 7, no. 2, 1969, pp 242-259.
14. S.I. Niculescu, Delay Effects on Stability: A Robust Control Approach, Springer-Verlag: Heidelberg, vol. 269, 2001.
15. N. Olgac, and R. Sipahi, An exact method for the stability analysis of time-delayed LTI systems, IEEE Trans. Automat. Contr., vol. 47, 2002, pp 793-797.
16. J. Sun, Multiple eigenvalue sensitivity analysis, Linear Algebra and Its Applications, vol. 137/138, 1990, pp 183-211.
17. K. Walton and J.E. Marshall, Direct Method for TDS Stability Analysis, IEE Proc. Contr. Theory & Appl., 134, Pt. D:2, 1987, pp 101-107.