The Lambert W function and the spectrum of some multidimensional time-delay systems

Automatica

Volumn 43, Issue 12, 2007, Pages 2124-2128

  Jarlebring, Elias ^a   Damm, Tobias ^b  

^a TECHNICAL UNIVERSITY OF BRAUNSCHWEIG   (Germany)

^b Rheinland Pfälzische Technische Universität Kaiserslautern Landau   (Germany)

Author keywords

Jordan canonical form; Lambert W function; Linear time delay systems; Matrix function; Simultaneous triangularization

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; FUNCTION EVALUATION; SPECTRUM ANALYSIS; TIME DELAY;

JORDAN CANONICAL FORM; LAMBERT W FUNCTION; LINEAR TIME-DELAY SYSTEMS; MATRIX FUNCTION; SIMULTANEOUS TRIANGULARIZATION;

DELAY CONTROL SYSTEMS;

EID: 36248972314     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2007.04.001     Document Type: Article

References (23)

1. Asl F.M., and Ulsoy A.G. Analysis of a system of linear delay differential equations. Journal of Dynamics System Measure and Control 125 (2003) 215-223
2. Bambi, M. (2006). Endogenous growth and time-to-build: The AK case. In 12th International conference on computers in economics and finance. EUI Working Paper, No. 2006/17.
3. Breda D., Maset S., and Vermiglio R. Pseudospectral differencing methods for characteristic roots of delay differential equations. SIAM Journal on Scientific Computing 27 2 (2005) 482-495
4. Chen, M., Abate, A., & Sastry, S. (2005). New congestion control schemes over wireless networks: Stability analysis. In Proceedings of the 16th IFAC world congress, Prague.
5. Chen Y., and Moore K. Analytical stability bound for a class of delayed fractional-order dynamical systems. Nonlinear Dynamics 29 (2002) 191-200
6. Chen Y., and Moore K. Analytical stability bound for delayed second-order systems with repeating poles using Lambert function W. Automatica 38 (2002) 891-895
7. Corless R., Gonnet G.H., Hare D.E.G., Jeffrey D.J., and Knuth D.E. On the Lambert W function. Advances in Computational Mathematics 5 (1996) 329-359
8. Engelborghs, K. (2000). DDE-BIFTOOL: A Matlab package for bifurcation analysis of delay differential equations. Technical report, Department of Computer Science, K.U. Leuven.
9. Hale, J. K., & Lunel, S. M. V. (1993). Introduction to functional differential equations, Applied mathematical sciences (Vol. 99). Berlin: Springer.
10. Heffernan J.M., and Corless R.M. Solving some delay differential equations with computer algebra. Mathematical Scientist 31 1 (2006) 21-34
11. Higham, N. (2006). Functions of matrices. In L. Hogben (Ed.), Handbook of linear algebra. Boca Raton, FL: CRC Press.
12. Horn R., and Johnson C.R. Topics in matrix analysis (1991), Cambridge University Press, Cambridge, UK
13. Hövel P., and Schöll E. Control of unstable steady states by time-delayed feedback methods. Physical Review E 72 (2005)
14. Hwang C., and Cheng Y.-C. A note on the use of the Lambert W function in the stability analysis of time-delay systems. Automatica 41 (2005) 1979-1985
15. Jeffrey D.J., Hare D.E.G., and Corless R.M. Unwinding the branches of the Lambert W function. Mathematical Scientist 21 (1996) 1-7
16. Kalmár-Nagy, T. (2005). A new look at the stability analysis of delay differential equations. In Proceedings of IDETC'05.
17. Pitcher, A. B., & Corless, R. M. (2005). Quasipolynomial root-finding: A numerical homotopy method. Technical report, Department of Applied Mathematics, University of Western Ontario.
18. Radjavi H., and Rosenthal P. Simultaneous triangularization (2000), Springer, New York
19. Shinozaki H., and Mori T. Robust stability analysis of linear time-delay systems by Lambert W function: Some extreme point results. Automatica 42 10 (2006) 1791-1799
20. Sontag E.D. Mathematical Control Theory: Deterministic Finite Dimensional Systems. (2nd ed.) (1998), Springer, New York
21. Wahi P., and Chatterjee A. Galerkin projections for delay differential equations. Transactions of the ASME 127 (2005) 80-86
22. Yi, S., & Ulsoy, A. G. (2006). Solution of a system of linear delay differential equations using the matrix Lambert function. In Proceedings of the 26th American control conference (pp. 2433-2438). Minneapolis.
23. Yi, S., Ulsoy, A. G., & Nelson, P. W. (2006). Analysis of systems of linear delay differential equations using the Lambert function and the Laplace transformation. Automatica, submitted for publication.