Conditioning of the stable, discrete-time Lyapunov operator

SIAM Journal on Matrix Analysis and Applications

Volumn 22, Issue 1, 2000, Pages 56-65

  Tippett, Michael K ^a   Cohn, Stephen E ^b   Todling, Ricardo ^b   Marchesin, Dan ^c  

^a Department of Earth and Environmental Sciences   (United States)

^b NASA GODDARD SPACE FLIGHT CENTER   (United States)

^c IMPA   (Brazil)

Author keywords

Condition estimates; Large scale systems; Lyapunov matrix equation; Radius of stability

Indexed keywords

EID: 0034353655     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479899354822     Document Type: Article

References (23)

1. R. BHATIA, Matrix Analysis, Springer-Verlag, New York, 1997.
2. R. BHATIA, A note on the Lyapunov equation, Linear Algebra Appl., 259 (1997), pp. 71-76.
3. K. M. BUTLER AND B. F. FARRELL, Three-dimensional optimal perturbations in viscous shear flow, Phys. Fluids A, 4 (1992), pp. 1637-1650.
4. R. BYERS AND S. NASH, On the singular "vectors" of the Lyapunov operator, SIAM J. Alg. Discrete Methods, 8 (1987), pp. 59-66.
5. S. E. COHN AND R. TODLING, Approximate data assimilation schemes for stable and unstable dynamics, J. Meteor. Soc. Japan, 74 (1996), pp. 63-75.
6. B. F. FARRELL AND P. J. IOANNOU, Generalized stability theory. Part I: Autonomous operators, J. Atmospheric Sci., 53 (1996), pp. 2025-2040.
7. P. M. GAHINET, A. J. LAUB, C. S. KENNEY, AND G. A. HEWER, Sensitivity of the stable discrete-time Lyapunov equation, IEEE Trans. Automat. Control, 35 (1990), pp. 1209-1217.
8. G. H. GOLUB AND C. F. VAN LOAN, Matrix Computations, 3rd ed., The Johns Hopkins University Press, Baltimore, MD, 1996.
9. P. L. HOUTEKAMER AND H. L. MITCHELL, Data assimilation using an ensemble Kalman filter technique, Monthly Weather Rev., 126 (1998), pp. 796-811.
10. I. M. JAIMOUKHA AND E. M. KASENALLY, Krylov subspace methods for solving large Lyapunov equations, SIAM J. Numer. Anal., 31 (1994), pp. 227-251.
11. R. E. KALMAN AND J. E. BERTRAM, Control system analysis and design via the "second method" of Lyapunov. II. Discrete-time systems, Trans. ASME Ser. D. J. Basic Engrg., 82 (1960), pp. 394-400.
12. S. R. KOLLA, Improved stability robustness bounds for digital control systems in state-space models, Internat. J. Control, 64 (1996), pp. 991-994.
13. P. LANCASTER, Explicit solutions of linear matrix equations, SIAM Rev., 12 (1970), pp. 544-566.
14. C. C. MACDUFFEE, The Theory of Matrices, Chelsea, New York, 1956.
15. T. MORI, On the relationship between the spectral, radius and the stability radius of discrete systems, IEEE Trans. Automat. Control, 35 (1990), p. 835.
16. T. MORI, N. FUKUMA, AND M. KUWAHARA, Upper and lower bounds for the solution to the discrete Lyapunov matrix equation, Internat. J. Control, 36 (1982), pp. 889-892.
17. A. OSTROWSKI, A quantitative formulation of Sylvester's law of inertia, Proc. Natl. Acad. Sci. USA, 45 (1959), pp. 740-744.
18. K. M. PRZYLUSKI, The Lyapunov equation and the problem of stability for linear bounded discrete-time systems in Hilbert space, Appl. Math. Optim., 6 (1980), pp. 97-112.
19. J.-G. SUN, Perturbation theory for algebraic Riccati equations, SIAM J. Matrix Anal. Appl., 19 (1998), pp. 39-65.
20. M. K. TIPPETT AND D. MARCHESIN, Upper bounds for the solution of the discrete algebraic Lyapunov equation, Automatica, 35 (1999), pp. 1485-1489.
21. L. N. TREFETHEN, Pseudospectra of linear operators, SIAM Rev., 39 (1997), pp. 383-406.
22. L. N. TREFETHEN, A. E. TREFETHEN, AND S. C. REDDY, Hydrodynamic stability without eigenvalues, Science, 261 (1993), pp. 578-584.
23. J. S. WHITAKER AND P. D. SARDESHMUKH, A linear theory of extratropical synoptic Eddy statistics, J. Atmospheric Sci., 55 (1998), pp. 237-258.