Matrix bounds of the solutions of the continuous and discrete Riccati equations - A unified approach

International Journal of Control

Volumn 76, Issue 6, 2003, Pages 635-642

  Lee, Chien Hua ^a  

^a CHENG SHIU UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

LYAPUNOV METHODS; MATRIX ALGEBRA; PERTURBATION TECHNIQUES; RICCATI EQUATIONS; SYSTEM STABILITY;

MATRIX BOUNDS;

CONTROL SYSTEMS;

EID: 0142168433     PISSN: 00207179     EISSN: None     Source Type: Journal    
DOI: 10.1080/0020717031000105580     Document Type: Article

References (30)

1. AMIR-MOEZ, R., 1956, Extreme properties of eigenvalues of a Hermitian transformation and singular values of the sum and product of linear transformations. Duke Mathematics Journal, 23, 463-467.
2. GARLOFF, J., 1986, Bounds for the eigenvalues of the solution of discrete Riccati and Lyapunov equations and the continuous Lyapunov equation. International Journal of Control, 43, 424-431.
3. KARANAM, V. R., 1982, Eigenvalue bounds for algebraic Riccati and Lyapunov equations. IEEE Transactions on Automatic Control, 27, 461-463.
4. KARANAM, V. R., 1983, A Note on eigenvalue bounds in algebraic Riccati equation. IEEE Transactions on Automatic Control, 28, 109-111.
5. KIM, S. W., and PARK, P. G., 1999, Matrix bounds of the discrete ARE solution. Systems and Control Letters, 36, 15-20.
6. KOMAROFF, N., 1992, Upper bounds for the solution of the discrete Riccati equation. IEEE Transactions on Automatic Control, 37, 1370-1373.
7. KOMAROFF, N., 1994, Iterative matrix bounds and computational solutions to the discrete algebraic Riccati equation. IEEE Transactions on Automatic Control, 39, 1676-1678.
8. KOMAROFF, N., and SHAHIAN, B., 1992, Lower summation bounds for the discrete Riccati and Lyapunov equations. IEEE Transactions on Automatic Control, 37, 1078-1080.
9. KOUIKOGLOU, V. S., and PHILLIS, Y. A., 1993, Trace bounds on the covariances of continuous-time systems with multiplicative noise. IEEE Transactions on Automatic Control, 38, 138-142.
10. KWON, B. H., YOUN, M. J., and BIEN, Z., 1985, On bounds of the Riccati and Lyapunov equations. IEEE Transactions on Automatic Control, 30, 1134-1135.
11. KWON, W. H., MOON, Y. S., and AHN, S. C., 1996, Bounds in algebraic Riccati and Lyapunov equations: a survey and some new results. International Journal of Control, 64, 377-389.
12. KWON, W. H., and PEARSON, A. E., 1977, A note on the algebraic matrix Riccati equation. IEEE Transactions on Automatic Control, 22, 143-144.
13. LEE, C. H., 1996, On the matrix bounds for the solution of the discrete algebraic Riccati equation. IEEE Transactions on Circuits and Systems - I, 43, 402-407.
14. LEE, C. H., 1997 a, On the upper and lower bounds of the solution for the continuous Riccato matrix equation. International Journal of Control, 66, 105-118.
15. LEE, C. H., 1997 b, Upper and lower bounds of the solution of the discrete algebraic Riccati and Lyapunov matrix equations. International Journal of Control, 68, 579-598.
16. LEE, C. H., 1997c, New results for the bounds of the solution for the continuous Riccati and Lyapunov equations. IEEE Transactions on Automatic Control, 42, 118-123.
17. LEE, C. H., 1998, Simple stabilizability criteria and memoryless state feedback control design for time-delay systems with time-varying perturbations. IEEE Transactions on Circuits and Systems - I, 45, 1121-1125.
18. LEE, C. H., and LEE, S. T., 2001, On the estimation of solution bounds of the generalized Lyapunov equations and the robust root clustering for the linear perturbed systems. International Journal of Control, 74, 996-1008.
19. LEE, C. H., LI, T.-H. S., and KUNG, F. C., 1993, A new approach for the robust stability of perturbed systems with a class of non-commensurate time delays. IEEE Transactions on Circuits and Systems - I, 40, 605-608.
20. MIDDLETON, R. H., and GOODWIN, G. C., 1990, Digital Control and Estimation: a Unified Approach (Englewood Cliffs, NJ: Prentice-Hall).
21. MORI, T., and DERESE, I. A., 1984, A brief summary of the bounds on the solution of the algebraic equations in control theory. International Journal of Control, 39, 247-256.
22. MORI, T., FUKUMA, N., and KUWAHARA, M., 1982, On the discrete Lyapunov matrix equation. IEEE Transactions on Automatic Control, 27, 463-464.
23. MORI, T., FUKUMA, N., and KUWAHARA, M., 1985, Eigen-value bounds for the discrete Lyapunov matrix equation. IEEE Transactions on Automatic Control, 30, 925-926.
24. MRABTI, M., and HMAMED, A., 1992, Bounds for the solution of the Lyapunov matrix equation - A unified approach. Systems and Control Letters, 18, 73-81.
25. TRAN, M. T., and SAWAN, M. E., 1984, A note on the discrete Lyapunov and Riccati matrix equations. International Journal of Control, 39, 337-341.
26. WANG, S. D., KUO, T. S., and HSU, C. F., 1986, Trace bounds on the solution of the algebraic matrix Riccati and Lyapunov equations. IEEE Transactions on Automatic Control, 31, 654-656.
27. WANG, S. S., and LIN, T. P., 1987, Robust stability of uncertain time-delay systems. International Journal of Control, 46, 963-976.
28. YADAVALLI, R. K., 1993, Robust root clustering for linear uncertain systems using generalized Lyapunov theory. Automatica, 29, 237-240.
29. YASUDA, K., and HIRAI, K., 1979, Upper and lower bounds on the solution of the algebraic Riccati equations. IEEE Transactions on Automatic Control, 24, 483-487.
30. YAZ, E., 1983, A priori bound for optimal stochastic control problem with multiplicative noise. Electronics Letters, 19, 1137-1139.