A general minimal residual Kylov subspace method for large-scale model reduction

IEEE Transactions on Automatic Control

Volumn 42, Issue 10, 1997, Pages 1422-1427

  Jaimoukha, Imad M ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Distance problem; GMRES; Large scale systems; Model reduction

Indexed keywords

ALGORITHMS; CONTROLLABILITY; LARGE SCALE SYSTEMS; MATHEMATICAL MODELS; MATRIX ALGEBRA; PROBLEM SOLVING; STATE SPACE METHODS;

ARNOLDI PROCESS; CONTROLLABILITY SUBSPACE; GENERAL MINIMAL RESIDUAL KRYLOV SUBSPACE (GMRES); LARGE SCALE MODEL REDUCTION; TWO BLOCK DISTANCE PROBLEM;

CONTROL SYSTEM ANALYSIS;

EID: 0031259374     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.633831     Document Type: Article

References (18)

1. M. M. M. Al-Husari, B. Hendel, I. M. Jaimoukha, E. M. Kasenally, D. J. N. Limebeer, and A. Portone, "Vertical stabilization of Tokamak plasmas," in Proc. 30th IEEE Conf. Dec. Contr., Brighton, U.K., 1991, pp. 1165-1170.
2. R. Barrett et al., Templates for the Solution of Linear Systems Building Blocks for Iterative Methods. Philadelphia: SIAM, 1994.
3. D. L. Boley and G. H. Golub, "The nonsymmetric Lanczos algorithm and controllability," Syst. Contr. Lett., vol. 16, pp. 97-105, 1991.
4. D. L. Boley, "Krylov space methods on state-space control models," Univ. Minnesota, CS Tech. Rep. TR92-18, 1992.
5. ∞ Control Theory, Lecture Notes in Control and Information Sci., vol. 88. Berlin: Springer-Verlag, 1987.
6. K. Glover, D. J. N. Limebeer, J. C. Doyle, E. M. Kasenally, and M. G. Safonov, "A characterization of all solutions to the four-block general-distance problem," SIAM J. Contr. Optim., vol. 29, pp. 283-324, 1991.
7. ∞ error bounds," Int. J. Contr., vol. 39, pp. 1115-1193, 1984.
8. G. H. Golub and C. F. Van Loan, Matrix Computations, 2nd ed. Baltimore, MD: John Hopkins Univ. Press, 1990.
9. I. M. Jaimoukha and E. M. Kasenally, "Krylov subspace methods for solving large Lyapunov equations," SIAM J. Numer. Anal., vol. 31, no. 1, pp. 227-251, 1994.
10. _, "Oblique projection methods for large scale model reduction," SIAM J. Matrix Anal. Appl., vol. 16, no. 2, pp. 602-627, 1995.
11. B. C. Moore, "Principal component analysis in linear systems Controllability, observability and mode reduction," IEEE Trans. Automat. Contr., vol. AC-26, pp. 17-31, 1981.
12. B. Parlett, "Reduction to tridiagonal form and minimal realizations," SIAM J. Matrix Anal. Appl., vol. 13, no. 2, pp. 567-593, 1992.
13. Y. Saad, "Krylov subspace methods on supercomputers," SIAM J. Sci. Stat. Comput., vol. 10, pp. 1200-1232, 1989.
14. _, "The Lanczos bi-orthogonalization algorithm and other oblique projection methods for solving large unsymmetric systems," SIAM Numer. Anal., vol. 19, no. 3, pp. 435-506, 1982.
15. P. Van Dooren, "The generalized eigenstructure problem in linear system theory," IEEE Trans. Automat. Contr., vol. AC-26, pp. 111-129, 1981.
16. _, "Numerical linear algebra techniques for large scale matrix problems in systems and control," in Proc. 31st IEEE Conf. Dec. Contr., Tucson, AZ, 1992, pp. 1933-1938.
17. J. C. Wlllems, "Least-squares stationary optimal control and the algebraic Riccati equation," IEEE Trans. Automat. Contr., vol. AC-16, pp. 621-634, 1971.
18. P. M. R. Wortelboer, "Balanced reduction of high-dimensional mechanical systems: A block-balancing approach," in Proc. 30th IEEE Conf. Dec. Contr., Brighton, U.K., 1991, pp. 1974-1975.