Solution of positive periodic discrete Lyapunov equations with applications to the balancing of periodic systems

ECC 1997 - European Control Conference

Volumn , Issue , 1997, Pages 3794-3799

  Varga, A ^a  

^a GERMAN AEROSPACE CENTER DLR   (Germany)

Author keywords

Balancing transformation; Linear time varying systems; Numerical methods; Periodic systems

Indexed keywords

LINEAR TRANSFORMATIONS; LYAPUNOV FUNCTIONS; MATHEMATICAL TRANSFORMATIONS; TIME VARYING SYSTEMS;

DISCRETE TIME; LINEAR TIME-VARYING SYSTEMS; LYAPUNOV EQUATION; MODEL REDUCTION; SCHUR DECOMPOSITION; SYLVESTER EQUATION;

NUMERICAL METHODS;

EID: 84949109999     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.23919/ecc.1997.7082708     Document Type: Conference Paper

References (12)

1. R. H. Bartels and G. W. Stewart. Algorithm 432: Solution of the matrix equation AX+XB=C. Comm. ACM, 15:820-826, 1972.
2. S. Bittanti, P. Colaneri, and G. De Nicolao. The difference periodic Riccati equation for the periodic prediction problem. IEEE Trans. Autom. Control, 33:706-712, 1988.
3. A. W. Bojanczyk, G. Golub, and P. Van Dooren. The periodic Schur decomposition. Algorithms and applications. In F. T. Luk, editor, Proceedings SPIE Conference, volume 1770, pages 31-42, July 1992.
4. P. E. Gill, G. H. Golub, W. Murray, and M. A. Saunders. Methods for modifying matrix factorizations. Math. Comput., 28:505-535, 1974.
5. G. H. Golub and C. F. Van Loan. Matrix Computations. John Hopkins University Press, Baltimore, 1989.
6. A. Halanay and V. Ionescu. Time-Varying Discrete Linear Systems. Birkhauser, 1994.
7. S. J. Hammarling. Numerical solution of the stable, non-negative definite Lyapunov equation. IMA J. Numer. Anal, 2:303-323, 1982.
8. J. J. Hench and A. J. Laub. Numerical solution of the discrete-time periodic Riccati equation. IEEE Trans. Autom. Control, 39:1197-1210, 1994.
9. T. Penzl. Numerical solution of generalized Lyapunov equations. Preprint SFB393/96-02, Technical University Chemnitz, May 1996.
10. J. Sreedhar and P. Van Dooren. Periodic Schur form and some matrix equations. In U. Helmke, R. Men-nicken, and J. Saurer, editors, Proc. MTNS'93, Re-gensburg, Germany, volume I, pages 339-362, 1993.
11. M. S. Tombs and I. Postlethwaite. Truncated balanced realization of a stable non-minimal state-space system. Int. J. Control, 46:1319-1330, 1987.
12. A. Varga and S. Pieters. A computational approach for optimal periodic output feedback control. In Proc. CACSD'96 Symposium, Dearborn, MI, pp. 176-181, 1996.