On solving discrete-time periodic riccati equations

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 38, Issue 1, 2005, Pages 354-359

  Varga, A ^a  

^a GERMAN AEROSPACE CENTER DLR   (Germany)

Author keywords

Deadbeat control; Numerical methods; Periodic systems; Riccati equation

Indexed keywords

NUMERICAL METHODS; TIME VARYING SYSTEMS;

DEADBEAT CONTROL; DISCRETE TIME; NON NEGATIVES; PERIODIC RICCATI EQUATION; QZ ALGORITHMS; SINGULAR CONTROL; SOFTWARE IMPLEMENTATION; STABILIZING SOLUTIONS;

RICCATI EQUATIONS;

EID: 79960702312     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20050703-6-cz-1902.00630     Document Type: Conference Paper

References (19)

1. Benner, P. and R. Byers (2001). Evaluating products of matrix pencils and collapsing matrix products. Numerical Linear Algebra with Applications 8, 357-380.
2. Benner, P., R. Byers, R. Mayo, E. S. Quintana-Orti and V. Hernandez (2002). Parallel algorithms for LQ optimal control of discrete-time periodic linear systems. Journal of Parallel and Distributed Computing 62, 306-325.
3. Bojanczyk, A. W., G. Golub and P. Van Dooren (1992). The periodic Schur decomposition. Algorithms and applications. Proceedings SPIE Conference (F. T. Luk, Ed.). Vol. 1770. pp. 31-42.
4. Chu, E.K.W., H.Y. Fan, W.W. Lin and C.S. Wang (2004). Structure-preserving algorithm for periodic discrete-time algebraic Riccati equations. Int. J. Control 77, 767-788.
5. Emami-Naeini, A. and G. F. Franklin (1982). Deadbeat control and tracking of discrete-time systems. IEEE Trans. Automat. Control 27, 176-181.
6. Golub, G. H. and C. F. Van Loan (1989). Matrix Computations. John Hopkins University Press. Baltimore.
7. Hench, J. J. and A. J. Laub (1994). Numerical solution of the discrete-time periodic Riccati equation. IEEE Trans. Automat. Control 39, 1197-1210.
8. Kressner, D. (2004). Numerical Methods and Software for General and Structured Eigenvalue Problems. PhD thesis. TU Berlin. Institut für Mathematik, Berlin, Germany.
9. Misra, P., P. Van Dooren and A. Varga (1994). Computation of structural invariants of generalized state-space systems. Automatica 30, 1921-1936.
10. Oarǎ, C. and A. Varga (1999). The general inner-outer factorization problem for discrete-time systems. Proc. of ECC'99, Karlsruhe, Germany.
11. Pittelkau, M. E. (1993). Optimal periodic control for spacecraft pointing and attitude determination. J. of Guidance, Control, and Dynamics 16, 1078-1084.
12. Van Dooren, P. (1981). A generalized eigenvalue approach for solving Riccati equations. SIAM J. Sci. Stat. Comput. 2, 121-135.
13. Van Dooren, P. (1999). Two point boundary value and periodic eigenvalue problems. Proc. of CACSD'99 Symposium, Kohala Coast, Hawaii.
14. Varga, A. (1999). Balancing related methods for minimal realization of periodic systems. Systems & Control Lett. 36, 339-349.
15. Varga, A. (2004a). Computation of Kalman decompositions of periodic systems. European Journal of Control 10, 1-8.
16. Varga, A. (2004b). Computation of Kronecker-like forms of periodic matrix pairs. Proc. of MTNS'04, Leuven, Belgium.
17. Varga, A. (2005). A PERIODIC SYSTEMS Toolbox for MATLAB. Prepr. of IFAC 2005 World Congress, Prague, Czech Republic.
18. Varga, A. and P. Van Dooren (2003). Computing the zeros of periodic descriptor systems. Systems & Control Lett. 50, 371-381.
19. Varga, A. and S. Pieters (1998). Gradient-based approach to solve optimal periodic output feedback control problems. Automatica 34, 477-481.