New upper matrix bounds for the solution of the continuous algebraic Riccati matrix equation

International Journal of Control, Automation and Systems

Volumn 6, Issue 5, 2008, Pages 776-784

  Davies, Richard Keith ^a   Shi, Peng ^a,b,c   Wiltshire, Ron ^a  

^a UNIVERSITY OF GLAMORGAN   (United Kingdom)

^b VICTORIA UNIVERSITY   (Australia)

^c UNIVERSITY OF SOUTH AUSTRALIA   (Australia)

Author keywords

Continuous algebraic riccati equation (CARE); Eigenvalue bound; Iterative algorithm; Matrix bound; Similarity transformation

Indexed keywords

DIFFERENTIAL EQUATIONS; ITERATIVE METHODS; RICCATI EQUATIONS;

CONTINUOUS ALGEBRAIC RICCATI EQUATION (CARE); EIGENVALUE BOUND; ITERATIVE ALGORITHM; MATRIX BOUND; SIMILARITY TRANSFORMATION;

MATRIX ALGEBRA;

EID: 53549094682     PISSN: 15986446     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (29)

1. W. H. Kwon and A. E. Pearson, "A note on the algebraic matrix Riccati equation," IEEE Trans. on Automatic Control, vol. 22, pp. 143-144, 1977.
2. R. V. Patel and M. Toda, "On norm bounds for algebraic Riccati and Lyapunov equations," IEEE Trans. on Automatic Control, vol. 23, pp. 87-88, 1978.
3. K. Yasuda and K. Hirai, "Upper and lower bounds on the solution of the algebraic Riccati equation," IEEE Trans. on Automatic Control, vol. 24, pp. 483-487, 1979.
4. V. Karanam, "Eigenvalue bounds for algebraic Riccati and Lyapunov equations," IEEE Trans. on Automatic Control, vol. 27, pp. 461-463, 1982.
5. V. Karanam, "A note on eigenvalue bounds in algebraic Riccati equations," IEEE Trans. on Automatic Control, vol. 28, pp. 109-111, 1983.
6. T. Mori and I. A. Deres, "A brief summary of the bounds on the solution of the algebraic matrix equations in control theory," International Journal of Control, vol. 39, pp. 247-256, 1984.
7. B. H. Kwon, M. J. Youn, and Z. Bien, "On bounds of the Riccati and Lyapunov matrix equations," IEEE. Trans. on Automatic Control, vol. 30, pp. 1134-1135, 1985.
8. T. Mori, "On some bounds in the algebraic Riccati equations," IEEE Trans. on Automatic Control, vol. 30, pp. 162-164, 1985.
9. E. Yaz, "Bounds for the eigenvalues of the solution matrix of the algebraic Riccati equation," International Journal of Systems Science, vol. 16, pp. 816-820, 1985.
10. S. D. Wang, T. S. Kuo, and C. F. Hsu, "Trace bounds on the solution of the algebraic matrix Riccati and Lyapunov equations," IEEE Trans. on Automatic Control, vol. 31, pp. 654-656, 1986.
11. N. Komaroff, "Simultaneous eigenvalue lower bounds for the Riccati matrix equation," IEEE Trans. on Automatic Control, vol. 34, pp. 175-177, 1989.
12. J. H. Kim and Z. Bien, "Some bounds of the solution of the algebraic Riccati equation," IEEE Trans. on Automatic Control, vol. 37, pp. 1209-1210, 1992.
13. N. Komaroff, "Diverse bounds for the eigenvalues of the continuous algebraic Riccati equation," IEEE Trans. on Automatic Control, vol. 39, pp. 532-534, 1994.
14. T. Kang, B. S. Kim, and J. G. Lee, "Spectral norm and trace bounds of algebraic matrix Riccati equations," IEEE Trans. on Automatic Control, vol. 41, pp. 1828-1830, 1996.
15. W. H. Kwon, Y. S. Moon, and S. C. Ann, "Bounds in algebraic Riccati and Lyapunov equations: A survey and some new results," International Journal of Control, vol. 64, pp. 377-389, 1996.
16. C. H. Lee, "New results for the bounds of the solution of the solution for the continuous Riccati and Lyapunov equations," IEEE Trans. on Automatic Control, vol. 42, pp. 118-123, 1997.
17. C. H. Lee, "On the upper and lower bounds of the solution for the continuous Riccati matrix equation," International Journal of Control, vol. 66, pp. 105-118, 1997.
18. H. H. Choi and T. Y. Kuc, "Lower matrix bounds for the continuous algebraic Riccati and Lyapunov matrix equations," Automatica, vol. 38, pp. 1147-1152, 2002.
19. C. H. Lee, "Solution bounds of the continuous Riccati matrix equation," IEEE Trans. on Automatic Control, vol. 48, pp. 1409-1413, 2003.
20. C. H. Lee, "New upper solution bounds of the continuous algebraic Riccati matrix equation," IEEE Trans. on Automatic Control, vol. 51, pp. 330-334, 2006.
21. D. S. Bernstein, Matrix Mathematics: Theory, Facts And Formulas With Application To Linear Systems Theory, Princeton University Press, 2005.
22. D. L. Kleinmann, "On an iterative technique for Riccati equation computations," IEEE Trans. on Automatic Control, vol. 13, pp. 114-115, 1968.
23. S. W. Kim and P. G. Park, "Upper solution bounds of the continuous ARE solution," IEICE Trans. on Fundamentals of Electronics, Communications and Computer Sciences, vol. E83A, pp. 380-385, 2000.
24. R. K. Davies, P. Shi, and R. J. Wiltshire, "New upper solution bounds of the discrete algebraic Riccati matrix equation," Journal of Computational and Applied Mathematics, vol. 213, no. 2, pp. 307-315, 2008.
25. R. K. Davies, P. Shi, and R. J. Wiltshire, "New lower solution bounds of the continuous algebraic Riccati matrix equation," Linear Algebra and its Applications, vol. 427, pp. 242-255, 2007.
26. K. Ogata, Modern Control Engineering, 3rd edition, Prentice Hall, 1997.
27. M. Basin, E. Sanchez, and R. Martinez-Zuniga, "Optimal linear filtering for systems with multiple state and observation delays," Int. J. of Innovative Computing, Information and Control, vol. 3, no. 5, pp. 1309-1320, 2007.
28. M. S. Mahmoud, Y. Shi, and H. N. Nounou, "Resilient observer-based control of uncertain time-delay systems," Int. J. of Innovative Computing, Information and Control, vol. 3, no. 2, pp. 407-418, 2007.
29. M. Hassan and K. Boukas, "Multilevel technique for large scale LQR with time-delays and systems constraints," Int. J. of Innovative Computing, Information and Control, vol. 3, no. 2, pp. 419-434, 2007.