Pseudospectra and stability radii for analytic matrix functions with application to time-delay systems

Linear Algebra and Its Applications

Volumn 418, Issue 1, 2006, Pages 315-335

  Michiels, Wim ^a   Green, Kirk ^b   Wagenknecht, Thomas ^b   Niculescu, Silviu Iulian ^c  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b UNIVERSITY OF BRISTOL   (United Kingdom)

^c UNIVERSITÉ DE TECHNOLOGIE DE COMPIÈGNE   (France)

Author keywords

Delay equations; Pseudospectrum; Robustness; Stability

Indexed keywords

COMPUTATIONAL METHODS; DIFFERENCE EQUATIONS; PERTURBATION TECHNIQUES; ROBUSTNESS (CONTROL SYSTEMS); STABILITY; SYSTEMS ANALYSIS; TIME DOMAIN ANALYSIS;

DELAY EQUATIONS; PSEUDOSPECTRUM; TIME-DELAY SYSTEMS;

MATRIX ALGEBRA;

EID: 33747836576     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2006.02.036     Document Type: Article

References (22)

1. Trefethen L., and Embree M. Spectra and Pseudospectra, the Behavior of Nonnormal Matrices and Operators (2005), Princeton University Press, Princeton, NJ
2. Trefethen L. Pseudospectra of linear operators. SIAM Rev. 39 3 (1997) 383-406
3. Hinrichsen D., and Pritchard A. Mathematical Systems Theory I. Modelling, State Space Analysis, Stability and Robustness. Texts in Applied Mathematics vol. 48 (2005), Springer Verlag, Berlin
4. Tisseur F., and Meerbergen K. The quadratic eigenvalue problem. SIAM Rev. 43 (2001) 235-286
5. Tisseur F., and Higham N. Structured pseudospectra for polynomial eigenvalue problems with applications. SIAM J. Matrix Anal. Appl. 23 1 (2001) 187-208
6. K. Green, T. Wagenknecht, Pseudospectra and delay differential equations, Journal of Computational and Applied Mathematics, in press.
7. Michiels W., and Roose D. An eigenvalue based approach for the robust stabilization of linear time-delay systems. Internat. J. Control 76 7 (2003) 678-686
8. Pappas G., and Hinrichsen D. Robust stability of linear systems described by higher order dynamic equations. IEEE Trans. Automat. Control 38 (1993) 1430-1435
9. Genin Y., Stefan R., and Van Dooren P. Real and complex stability radii of polynomial matrices. Linear Algebra Appl. 351-352 (2002) 381-410
10. Zhou K., Doyle J., and Glover K. Robust and Optimal Control (1996), Prentice Hall, Upper Saddle River, NJ
11. Michiels W., Engelborghs K., Roose D., and Dochain D. Sensitivity to infinitesimal delays in neutral equations. SIAM J. Control Optim. 40 4 (2002) 1134-1158
12. Hale J., and Verduyn Lunel S. Introduction to Functional Differential Equations. Applied Mathematical Sciences vol. 99 (1993), Springer Verlag, Berlin
13. Burke J., Lewis A., and Overton M. Optimization and pseudospectra, with applications to robust stability. SIAM J. Matrix Anal. Appl. 25 (2003) 80-104
14. P. Van Dooren, V. Vermaut, On stability radii of generalized eigenvalue problems, in: Proceedings of the 1997 European Control Conference (ECC'97), Brussels, Belgium, 1997.
15. Curtain R., and Pritchard A. Functional Analysis in Modern Applied Mathematics (1977), Academic Press, London
16. Gallestey E., Hinrichsen D., and Pritchard A. Spectral value sets of closed linear operators. Proc. R. Soc. Lond. A 456 (2000) 1397-1418
17. Byers R. A bisection method for measuring the distance of a stable matrix to the unstable matrices. SIAM J. Sci. Stat. Comp. 9 9 (1988) 875-881
18. ∞-norm. Systems Control Lett. 15 (1990) 1-7
19. ∞ norm of a transfer matrix and related problems. Math. Control Signals Systems 2 (1989) 207-219
20. ∞-norms and related questions, in: Proceedings of MTNS 1998, Padova, Italy, 1998, pp. 429-432.
21. Golub G., and Van Loan C. Matrix Computations. second ed. (1993), John Hopkins University Press, Baltimore
22. K. Engelborghs, T. Luzyanina, G. Samaey, DDE-BIFTOOL v. 2.00: a Matlab package for bifurcation analysis of delay differential equations, TW Report 330, Department of Computer Science, Katholieke Universiteit Leuven, Belgium, October 2001.