Solution of a system of linear delay differential equations using the matrix lambert function

Proceedings of the American Control Conference

Volumn 2006, Issue , 2006, Pages 2433-2438

  Sun, Yi ^a   Ulsoy, A G ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTION EVALUATION; MATRIX ALGEBRA; NUMERICAL METHODS; ORDINARY DIFFERENTIAL EQUATIONS; STATE ESTIMATION;

DELAY DIFFERENTIAL EQUATIONS (DDE); LAMBERT FUNCTIONS; STATE TRANSITION MATRIX;

LINEAR CONTROL SYSTEMS;

EID: 33751298298     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (12)

1. Gorecki H., Fuksa, S., Grabowski, P., and Korytowski, A., Analysis and Synthesis of Time Delay Systems, John Wiley and Sons, PWN-Polish Scientific Publishers Warszawa, 1989
2. R.E. Bellman and K.L. Cooke, Difference-Difference Equations, Academic Press, 1963
3. Lam, J., "Model Reduction of Delay Systems Using Pade Approximants," Int. J. Control, Vol. 57, No. 2, pp. 377-391, 1993
4. Golub, G. H., and Van Loan, C. F., Matrix Computations, Johns Hopkins Univ. Press, Baltimore, 1989
5. Falbo, C. E., "Analytic and Numerical Solutions to the Delay Differential Equations," Joint Meeting of the Northern and Southern California Sections of the MAA, San Luis Obispo, CA, 1995
6. Wright, E. M., "The Non-Linear Difference-Differential Equation," Q. J. Math., Vol. 17, pp. 245-252, 1946
7. Wright, E. M, "The Linear Difference-Differential Equation With Asymptotically Constant Coefficients," Am. J. Math., Vol. 70, No. 2, pp. 221-238, 1948
8. Asl, F.M., and Ulsoy, A.C., "Analysis of a System of Linear Delay Differential Equations," ASME J. Dynamic Systems, Measurement and Control, Vol. 125, No. 2, pp 215-223, 2003
9. Corless, R. M, Gonnet, G. H. Gonnet, D.E.G. Hare, and D.J. Jeffrey, "On Lambert's W Function", Technical Report, Dept. of Applied Math., Univ. of Western Ontario, London, Ontario, Canada
10. Lee T. N. and S. Dianat, "Stability of Time-Delay Systems", IEEE Trans. Aut. Control, Vol. AC-26, No. 4, pp. 951-953, 1981
11. H. Shinozaki, Robust Stability Analysis of Linear Time-Delay Systems by Lambert W Function. Master thesis, Dept. Electro. Inform. Sci., Kyoto Institute of Technology, Kyoto, Japan, 2003
12. Malek-zavarei, M., Jamshidi, M., Time-delay systems, North Holland, New York, 1987