Analysis and control of time delayed systems via the Lambert W function

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 17, Issue 1 PART 1, 2008, Pages

  Yi, Sun ^a   Nelson, Patrick W ^a   Ulsoy, A Galip ^a  

^a NONE

Author keywords

Gain scheduling; Nonlinear systems; Vibration and modal analysis

Indexed keywords

ANALYTICAL SOLUTIONS; DELAY DIFFERENTIAL EQUATIONS; DELAY TIME; EIGEN-VALUE; EIGENSPECTRUM; EIGENVALUE ASSIGNMENT; GAIN SCHEDULING; INFINITE SERIES; LAMBERT W FUNCTION; MATRIX; RESEARCH RESULTS; STABILITY ANALYSIS; TIME-DELAY SYSTEMS; TIME-DELAYED SYSTEMS; VIBRATION AND MODAL ANALYSIS;

EIGENVALUES AND EIGENFUNCTIONS; MODAL ANALYSIS; NONLINEAR SYSTEMS; ORDINARY DIFFERENTIAL EQUATIONS; SCHEDULING; TIME DELAY; VIBRATION ANALYSIS;

DELAY CONTROL SYSTEMS;

EID: 79961019952     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20080706-5-KR-1001.1153     Document Type: Conference Paper

References (26)

1. F. M. Asl and A. G. Ulsoy Analysis of a system of linear delay differential equations. J. Dyn. Syst. Meas. Control, 125:215-223, 2003.
2. H. T. Banks and A. Manitius Projection series for retarded functional differental equations with applications to optimal control problems. J. Differ. Equ., 18:296-332, 1975.
3. R. E. Bellman and K. L. Cooke. Differential-Difference Equations. Academic Press, New York, 1963.
4. S. G. Chen, A. G. Ulsoy and Y. Koren , Analysis of a system of linear delay differential equations, J. Dyn. Syst. Meas. Control, 119:457-460, 1997.
5. R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey and D. E. Knuth. On the Lambert W function. Adv. Comput. Math., 5:329 359, 1996.
6. K. Engelborghs, M. Dambrine, and D. Roose. Limitations of a class of stabilization methods for delay systems IEEE Trans. Auto. Cont., 46:336-339, 2001. @
7. J. K. Hale and S. M. V. Lunel. Introduction to Functional Differential Equations. Springer-Verlag, New York, 1993.
8. S. Holford and P. Agathoklis. Use of model reduction techniques for designing IIR filters with linear phase in the passband. IEEE Trans. Signal Process., 44:2396-2404, 1996.
9. W. S. Lu, E. B. Lee and Q. T. Zhang. Balanced approximation of two-dimensional and delay-differential systems. Int. J. Control, 46:2199-2218, 1987.
10. S. M. V. Lunel. Exponential Type Calculus for Linear Delay Equations. Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands, 1989.
11. M. Malek-Zavarei and M. Jamshidi. Time-Delay Systems: Analysis, Optimization, and Applications. Elsevier Science Pub., New York, 1987.
12. B. C. Moore. Principal component analysis in linear systems: controllability, observability, and model reduction. IEEE Trans. Aut. Cont., 26:17-32, 1981.
13. J. P. Richard. Time-delay systems: an overview of some recent advaces and open problems. Automatica, 39:1667 1964, 2003.
14. H. Shinozaki and T. Mori Robust stability analysis of linear time-delay systems by LambertWfunction: Some extreme point results. Automatica, 42:1791 1799, 2006.
15. G. J. Silva, A. Datta, and S. P. Bhattacharyya. Controller design via Pad approximation can lead to instability. in Proc. 40th IEEE Conf. on Decision and Control, 4733-4737, 2001.
16. E. D. Sontag Non-Linear Regulation - the piecewise linear approach. IEEE Trans. Aut. Cont., 26:346-358, 1981.
17. A. C. Tsoi. Recent advances in the algebraic system theory of delay differential equations. in Recent Theoretical Developments in Control M. J. Gregson, Ed. New York: Academic Press, 67-127, 1978.
18. H. F. Vandevenne. Controllability and stabilizability properties of delay systems. in Proc. 1972 IEEE Conf. on Decision Control and 11th Symp. on Adaptive Processes, New Orleans, LA, Dec., 370-377, 1972.
19. E. I. Verriest and T. Kailath. On generalized balanced realizations. IEEE Trans. Aut. Cont., 28:833-844, 1983.
20. S. Yi and A. G. Ulsoy. Solution of a system of linear delay differential equations using the matrix lambert function. in Proc. 2006 American Control Conference, 2433-2438, 2006.
21. S. Yi, P. W. Nelson and A. G. Ulsoy. Solution of systems of linear delay differential equations via Laplace transformation. in Proc. 45th IEEE Conf. on Decision and Control, 2535-2540, 2006.
22. S. Yi, P. W. Nelson and A. G. Ulsoy. Delay differential equations via the matrix Lambert W function and bifurcation analysis: Application to machine tool chatter. Math. Biosci. Eng, 4:355-368, 2007.
23. S. Yi, P. W. Nelson and A. G. Ulsoy. Survey on analysis of time delayed systems via the Lambert W function. Dyn. Contin. Discret. Impuls. Syst. Ser. A-Math Anal., 14(S2):296-301, 2007.
24. S. Yi, P. W. Nelson and A. G. Ulsoy. Controllability and observability of systems of linear delay differential equations via the matrix Lambert W function. IEEE Trans. Aut. Cont. 53:854-860, 2008.
25. S. Yi, P. W. Nelson and A. G. Ulsoy. Eigenvalue assignment via the Lambert W function for control for timedelay systems. J. Vib. Control, 2008 (in press).
26. S. Yi, P. W. Nelson and A. G. Ulsoy. Robust control and time-Domain specifications for systems for delay differential equations via eigenvalue assignment. in Proc. 2008 American Control Conference, 2008 (accepted).