On stability crossing curves for general systems with two delays

Journal of Mathematical Analysis and Applications

Volumn 311, Issue 1, 2005, Pages 231-253

  Gu, Keqin ^a   Niculescu, Silviu Iulian ^b   Chen, Jie ^c  

^a SOUTHERN ILLINOIS UNIVERSITY EDWARDSVILLE   (United States)

^b UNIVERSITÉ DE TECHNOLOGIE DE COMPIÈGNE   (France)

^c University of California Riverside   (United States)

Author keywords

Difference differential equations; Quasipolynomial; Stability; Time delay

Indexed keywords

EID: 24744452843     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2005.02.034     Document Type: Article

References (32)

1. R.E. Bellman K.L. Cooke Differential-Difference Equations 1963 Academic Press New York
2. E. Beretta Y. Kuang Geometric stability switch criteria in delay differential systems with delay dependent parameters SIAM J. Math. Anal. 33 2002 1144-1165
3. J. Bélair S.A. Campbell Stability and bifurcations of equilibria in a multiple-delayed differential equation SIAM J. Appl. Math. 54 1994 1402-1424
4. J.W. Bruce P.J. Giblin Curves and Singularities 1992 Cambridge Univ. Press
5. J. Chen H.A. Latchman Frequency sweeping tests for stability independent of delay IEEE Trans. Automat. Control 40 1995 1640-1645
6. J. Chen G. Gu C.N. Nett A new method for computing delay margins for stability of linear delay systems Systems Control Lett. 26 1995 101-117
7. K.L. Cooke Z. Grossman Discrete delay, distributed delay and stability switches J. Math. Anal. Appl. 86 1982 592-627
8. K.L. Cooke P. van den Driessche On zeroes of some transcendental equations Funkcial. Ekvac. 29 1986 77-90
9. R. Datko A procedure for determination of the exponential stability of certain differential-difference equations Quart. Appl. Math. 36 1978 279-292
10. O. Diekmann S.A. van Gils S.M. Verduyn-Lunel H.-O. Walther Delay Equations, Functional-, Complex and Nonlinear Analysis Appl. Math. Sci. vol. 110 1995 Springer-Verlag New York
11. L.E. El'Sgol'ts S.B. Norkin Introduction to the Theory and Application of Differential Equations with Deviating Arguments 1973 Academic Press New York
12. H. Górecki S. Fuksa P. Grabowski A. Korytowski Analysis and Synthesis of Time-Delay Systems 1989 Polish Scientific Publishers Warszawa
13. K. Gu V.L. Kharitnov J. Chen Stability of Time-Delay Systems 2003 Birkhäuser Boston
14. K. Gu, S.-I. Niculescu, J. Chen, On calculating the maximum radius of delay deviation, in: Sixteenth International Symposium on Mathematical Theory of Networks and Systems, Leuven, Belgium, July 5-9, 2004
15. H.W. Guggenheimer Differential Geometry 1977 Dover New York
16. J.K. Hale W. Huang Global geometry of the stable regions for two delay differential equations J. Math. Anal. Appl. 178 1993 344-362
17. J.K. Hale E.F. Infante F.-S.P. Tsen Stability in linear delay equations J. Math. Anal. Appl. 105 1985 535-555
18. J.K. Hale S.M. Verduyn Lunel Introduction to Functional Differential Equations Appl. Math. Sci. vol. 99 1993 Springer-Verlag New York
19. V.B. Kolmanovskii V.R. Nosov Stability of Functional Differential Equations Math. Sci. Engrg. vol. 180 1986 Academic Press New York
20. Y. Kuang Delay Differential Equations with Applications in Population Dynamics 1993 Academic Press Boston
21. N. Levinson R.M. Redheffer Complex Variables 1970 Holden-Day Baltimore
22. S.I. Niculescu Delay Effects on Stability-A Robust Control Approach Lecture Notes in Comput. Sci. vol. 269 2001 Springer-Verlag Heidelberg
23. S.I. Niculescu On delay robustness of a simple control algorithm in high-speed networks Automatica 38 2002 885-889
24. R. Nussbaum Differential delay equations with two time lags Mem. Amer. Math. Soc. 205 1978
25. N. Olgac R. Sipahi An exact method for the stability analysis of time-delayed LTI systems IEEE Trans. Automat. Control 47 2002 793-797
26. S. Ruan J. Wei On the zeros of transcendental functions with applications to stability of delay differential equations with two delays Dynam. Contin. Discrete Impuls. Systems 10 2003 863-874
27. Z.V. Rekasius, A stability test for systems with delays, Proc. of Joint Automatic Control Conf., Paper No. TP9-A, 1980
28. G. Stépán Retarded Dynamical Systems: Stability and Characteristic Function 1989 Wiley New York
29. G. Stépán Delay-differential equation models for machine tool chatter in: F.C. Moon (Eds) Dynamics and Chaos in Manufacturing Process 1998 Wiley New York 165-192
30. R. Sipahi, N. Olgac, Stability analysis of multiple time delay systems using the direct method, Paper #41495, ASME IMECE, Washington, DC, November 2003
31. R. Sipahi, N. Olgac, A novel stability study on multiple time-delay systems (MTDS) using the root clustering paradigm, in: American Control Conference, Boston, June 30-July 2, 2004
32. K. Walton J.E. Marshall Direct method for TDS stability analysis IEE Proc. Pt. D 134 1987 101-107