Closed-form solutions to the matrix equation AX - EXF = by with F in companion form

International Journal of Automation and Computing

Volumn 6, Issue 2, 2009, Pages 204-209

  Zhou, Bin ^a   Duan, Guang Ren ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Closed form solutions; Companion matrix; Descriptor linear systems; Linear matrix equations; Right factorizations

Indexed keywords

CLOSED-FORM SOLUTIONS; COMPANION MATRIX; DESCRIPTOR LINEAR SYSTEMS; LINEAR MATRIX EQUATIONS; RIGHT FACTORIZATIONS;

FACTORIZATION; LINEAR SYSTEMS;

MATRIX ALGEBRA;

EID: 65449142920     PISSN: 14768186     EISSN: 17518520     Source Type: Journal    
DOI: 10.1007/s11633-009-0204-6     Document Type: Article

References (26)

1. R. K. Gavin S. P. Bhattacharyya 1983 Robust and Well-conditioned Eigenstructure Assignment via Sylvester's Equation Optimal Control Applications and Methods 4 3 205 212 (Pubitemid 13604840)
2. B. H. Kwon M. J. Youn 1987 Eigenvalue-generalized Eigenvector Assignment by Output Feedback IEEE Transactions on Automatic Control 32 5 417 421 (Pubitemid 17582714)
3. J. Lam W. Y. Yan 1997 Pole Assignment with Optimal Spectral Conditioning Systems & Control Letters 29 5 241 253 (Pubitemid 127666630)
4. J. Lam W. Y. Yan T. Hu 1999 Pole Assignment with Eigenvalue and Stability Robustness International Journal of Control 72 13 1165 1174 (Pubitemid 30510912)
5. G. R. Duan 1993 Solutions to Matrix Equation AV + BW = V F and Their Application to Eigenstructure Assignment in Linear Systems IEEE Transactions on Automatic Control 38 2 276 280 (Pubitemid 23647777)
6. D. G. Luenberger 1964 Observing the State of a Linear System IEEE Transactions on Military Electronics 8 2 74 80
7. D. G. Luenberger 1971 An Introduction to Observers IEEE Transactions on Automatic Control 16 6 596 602
8. B. Zhou G. R. Duan Y. L. Wu 2008 Parametric Approach for the Normal Luenberger Function Observer Design in Second-order Descriptor Linear Systems International Journal of Automation and Computing 5 2 125 131
9. C. C. Tsui 1988 New Approach to Robust Observer Design International Journal of Control 47 3 745 751 (Pubitemid 18592182)
10. J. Park G. Rizzoni 1994 An Eigenstructure Assignment Algorithm for the Design of Fault Detection Filters IEEE Transactions on Automatic Control 39 7 1521 1524
11. J. Chen R. J. Patton H. Y. Zhang 1996 Design of Unknown Input Observers and Robust Fault Detection Filters International Journal of Control 63 1 85 105 (Pubitemid 126519369)
12. G. R. Duan R. J. Patton 2001 Robust Fault Detection Using Luenberger-type Unknown Input Observers - A Parametric Approach International Journal of Systems 32 4 533 540
13. J. Lam H. K. Tam 1997 Regional Pole Assignment with Eigenstructure Robustness International Journal of Systems Science 28 5 507 515 (Pubitemid 127650974)
14. J. Lam H. K. Tam 1997 Robust Partial Pole-placement via Gradient Flow Optimal Control Applications and Methods 18 5 371 379 (Pubitemid 127714567)
15. A. Saberi, A. A. Stoorvogel, P. Sannuti. Control of Linear Systems with Regulation and Input Constraints, in series of Communications and Control Engineering, Springer-Verlag, New York, USA, 1999.
16. A. Jameson 1968 Solution of the Equation AX + XB = C by Inversion of an M × M or N × N Matrix SIAM Journal on Applied Mathematics 16 5 1020 1023
17. C. C. Tsui 1987 A Complete Analytical Solution to the Equation TA - FT = LC and Its Applications IEEE Transactions on Automatic Control 32 8 742 744 (Pubitemid 17631965)
18. C. C. Tsui 1993 On the Solution to Matrix Equation TA - FT = LC and Its Applications SIAM Journal of Matrix Analysis and Applications 14 1 34 44
19. G. R. Duan 1996 On the Solution to Sylvester Matrix Equation AV + BW = EV F IEEE Transactions on Automatic Control 41 4 612 614 (Pubitemid 126768472)
20. B. Zhou G. R. Duan 2005 An Explicit Solution to the Matrix Equation AX - XF = BY Linear Algebra and its Applications 402 345 366 (Pubitemid 20656429)
21. G. R. Duan 1992 Solution to Matrix Equation AV + BW = EV F and Eigenstructure Assignment for Descriptor Systems Automatica 28 3 639 643
22. C. C. Tsui 2004 An Overview of Applications and Solutions of a Fundamental Matrix Equation Pair Journal of Franklin Institute 341 6 465 475
23. C. C. Tsui. Modern Control Systems Design Theories New Development, 2nd Edition, Science Press, Beijing, PRC, 2007. (in Chinese)
24. D. Z. Zheng. Linear System Theory, Tsinghua University Press, Beijing, PRC, 2002. (in Chinese).
25. G. R. Duan B. Zhou 2005 An Explicit Solution to Right Factorization with Application in Eigenstructure Assignment Journal of Control Theory and Applications 3 3 275 279
26. T. Kailath. Linear Systems, Prentice-Hall, Inc., Englewood Cliffs, NJ, USA, 1980.