Upper bounds for the solution of the discrete algebraic Lyapunov equation

Automatica

Volumn 35, Issue 8, 1999, Pages 1485-1489

  Tippett, Michael K ^a   Marchesin, Dan ^b  

^a Centra Previsao Tempo/Estud C   (Brazil)

^b IMPA   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

DISCRETE TIME CONTROL SYSTEMS; EIGENVALUES AND EIGENFUNCTIONS; LINEAR SYSTEMS; MATRIX ALGEBRA; SYSTEM STABILITY;

MATRIX LYAPUNOV EQUATION; PSEUDOSPECTRUM; RADIUS OF STABILITY; UPPER BOUNDS;

LYAPUNOV METHODS;

EID: 0033177761     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0005-1098(99)00041-2     Document Type: Article

References (18)

1. Buizza, R., Gelaro, R., Molteni, F., & Palmer, T. N. (1997). The impact of increased resolution on predictability studies with singular vectors. Quarterly Journal of Royal Meteorological Society, 123, 1007-1033.
2. Cohn, S. E. (1997). An introduction to estimation theory. Journal of Meteorological Society of Japan, 75, 257-288.
3. Farrell, B. F. (1988). Optimal excitation of neutral Rossby waves. Journal of Atmospheric Science, 42, 163-172.
4. Gahinet, P. M., Laub, A. J., Kenney, C. S., & Hewer, G. A. (1990). Sensitivity of the stable discrete-time Lyapunov equation. IEEE Transactions Automatic Control, 35, 1209-1217.
5. Gajić, Z., & Qureshi, M. (1995). Lyapunov Matrix Equation in System Stability and Control (255 pp.). San Diego: Academic Press.
6. Golub, G. H., & Van Loan, C. F. (1996). Matrix Computations (Third Ed.) (694 pp.). Baltimore: The Johns Hopkins University Press.
7. Ipsen, I. (1997). Computing an eigenvalue with inverse iteration. SIAM Review, 39, 254-291.
8. Kolla, S. R. (1996). Improved stability robustness bounds for digital control systems in state-space models. Internation Journal of Control, 64, 991-994.
9. Kwon, W. H., Moon, Y. S., & Ahn, S. C. (1996). Bounds in algebraic Riccati and Lyapunov equations: A survey and some new results. International Journal of Control, 64, 377-389.
10. Lancaster, P. (1970). Explicit solutions of linear matrix equations. SIAM Review, 12, 544-566.
11. Lee, C.-H. (1996). Upper and lower matrix bounds of the solution for the discrete Lyapunov equation. IEEE Transactions Automatic Control, 41, 1338-1341.
12. Liu, S. H. (1997). Computation of pseudospectra by continuation. SIAM Journal on Scientific Computing, 18, 565-573.
13. Mori, T. (1990). On the relationship between the spectral radius and the stability radius of discrete systems. IEEE Transactions Automatic Control, 35, 835.
14. Penland, C. (1989). Random forcing and forecasting using principal oscillation pattern analysis. Monthly Weather Review, 117, 2165-2185.
15. Tippett, M. K. (1998). Bounds for the solution of the discrete Lyapunov equation. Automatica, 34, 275-277.
16. Trefethen, L. N. (1997). Pseudospectra of linear operators. SIAM Review, 39, 383-406.
17. Trefethen, L. N., Trefethen, A. E., & Reddy, S. C. (1993). Hydrodynamic stability without eigenvalues. Science, 261, 578-584.
18. Whitaker, J. S., & Sardeshmukh, P. D. (1998). A linear theory of extratropical synoptic eddy statistics. Journal of Atmospheric Science, 55, 237-258 .