Solutions to generalized Sylvester matrix equation by Schur decomposition

International Journal of Systems Science

Volumn 38, Issue 5, 2007, Pages 369-375

  Zhou, Bin ^a   Duan, Guang Ren ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

General parametric solutions; Generalized Sylvester matrix equations; Schur decomposition; Singular value decomposition; Unimodular transformation

Indexed keywords

COMPUTATIONAL METHODS; CONTROL SYSTEM ANALYSIS; MACHINE DESIGN; MATHEMATICAL TRANSFORMATIONS; PARAMETER ESTIMATION; PROBLEM SOLVING;

CONTROL SYSTEM THEORY; SCHUR DECOMPOSITION; UNIMODULAR TRANSFORMATION;

SINGULAR VALUE DECOMPOSITION;

EID: 34249092654     PISSN: 00207721     EISSN: 14645319     Source Type: Journal    
DOI: 10.1080/00207720601160215     Document Type: Article

References (22)

1. N. F. Almuthairi and S. Bingulac, "On coprime factorization and minimal realization of transfer-function matrices using pseudoobservability concept", Int. J. Sys. Sci., 25, pp. 1819-1844, 1994.
2. T.G.J. Beelen and G.W. Veitkamp, "Numerical computation of a coprime factorization of a transfer-function matrix", Sys. Contr. Lett., 9, pp. 281-288, 1987.
3. J. Chen, R. Patton and H. Zhang, "Design unknown input observers and robust fault detection filters", Int. J. Contr., 63, pp. 85-105, 1996.
4. E.K. Chu and B.N. Datta, "Numerically robust pole assignment for second-order systems", Int. J. Contr., 64, pp. 1113-1127, 1996.
5. G.R. Duan, "Solution to matrix equation AV + BW = EV F and eigenstructure assignment for descriptor systems", Automatica, 28, pp. 639-643, 1992.
6. G.R. Duan, "Solutions to matrix equation AV + BW = V F and their application to eigenstructure assignment in linear systems", IEEE Trans. Autom. Contr., 38, pp. 276-280, 1993.
7. G.R. Duan, "On the solution to Sylvester matrix equation AV + BW = EV F", IEEE Trans. Autom. Contr., AC-41, pp. 612-614, 1996.
8. G.R. Duan and O.P. Liu, "Complete parametric approach for eigenstructure assignment in a class of second-order linear systems", Automatica, 38, pp. 725-729, 2002.
9. G.R. Duan and R.J. Patton, "Robust fault detection using Luenberger - type unknown input obsververs - a parametric approach", Int. J. Sys. Sci., 32, pp. 533-540, 2001.
10. K.R. Gavin and S.P. Bhattacharyya, "Robust and well-conditioned eigenstructure assignment via Sylvester's equation", Proc. Amer. Contr. Conf., 1982.
11. B.H. Kwon and M.J. Youn, "Eigenvalue-generalized eigenvector assignment by output feedback", IEEE Trans. Autom. Contr., AC-32, pp. 417-421, 1987.
12. D.J. Inman and A. Kress, "Eigenstructure assignment algorithm for second-order systems", J. Guid., Contr. Dyn., 22, pp. 729-731, 1999.
13. Y. Kim and H.S. Kim, "Eigenstructure assignment algorithm for mechanical second-order systems", J. Guid., Contr. Dyn., 22, pp. 729-731, 1999.
14. D.G. Luenberer, "Observing the state of a linear system", IEEE Trans. Mil., Electr., MI-8, pp, 74-80, 1964.
15. D.G. Luenberger, "An introduction to observers", IEEE Trans. Autom. Contr., 16, pp. 596-602, 1971.
16. J. Park and G. Rizzoni, "An cigcnstructure assignment algorithm for the design of fault detection filters", IEEE Trans. Autom. Contr., 39, pp. 1521-1524, 1994.
17. F. Rincon, "Feedback stabilization of second-order models", PhD dissertation, Northern Illinois University, De Kalb, Illinois, USA, 1992.
18. C.C. Tsui, "A complete analytical solution to the equation TA - FT=LC and its applications", IEEE Trans. Autom, Contr., AC-32, pp. 742-744, 1987
19. C.C. Tsui, "New approach to robust observer design", Int. J. Contr., 47, pp. 745-751, 1988.
20. C.C. Tsui, "On the solution to matrix equation TA - FT= LC and its applications", SIAM J. Matr. Anal. App., 14, pp. 34-44, 1993.
21. J.H. Wilkinson, Algebraic Eigenvalue Problem, New York: Oxford University Press, 1965.
22. B. Zhou and G.R. Duan, "An explicit solution to the matrix equation AX-XF = BY", Lin. Alg. App., 402, pp. 345-366, 2005.