Structural decomposition and its properties of linear multivariable singular systems

Journal of Systems Science and Complexity

Volumn 20, Issue 2, 2007, Pages 198-214

  He, Minghua ^a   Chen, Ben M ^b   Lin, Zongli ^c  

^a FUZHOU UNIVERSITY   (China)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^c UNIVERSITY OF VIRGINIA   (United States)

Author keywords

Descriptor systems; Singular systems; Structural invariants; System decomposition

Indexed keywords

DESCRIPTOR SYSTEMS; SINGULAR SYSTEMS; STRUCTURAL INVARIANTS; SYSTEM DECOMPOSITION;

DECOMPOSITION; DYNAMICS; LINEAR SYSTEMS; PROBLEM SOLVING; REDUNDANCY; STRUCTURAL PROPERTIES;

MULTIVARIABLE SYSTEMS;

EID: 34249013811     PISSN: 10096124     EISSN: 15597067     Source Type: Journal    
DOI: 10.1007/s11424-007-9017-2     Document Type: Conference Paper

References (22)

1. F. L. Lewis, A survey of linear singular systems, Circuits, Systems, and Signal Processing, 1986, 5: 3-36.
2. L. Dai, Singular Control System, Springer-Verlag, Berlin, 1989.
3. M. Kuijper, First Order Representations of Linear Systems, Birkhauser, Boston, 1994.
4. D. L. Chu and D. W. C. Ho, Necessary and sufficient conditions for the output feedback regularization of descriptor systems, IEEE Transactions on Automatic Control, 1999, 44: 405-412.
5. D. L. Chu and V. Mehrmann, Disturbance decoupling for descriptor systems by state feedback, SIAM Journal on Control and Optimization, 2000, 38: 1830-1858.
6. M. Fliess, Some basic structural properties of generalized linear systems, Systems & Control Letters, 1990, 15: 391-396.
7. T. Geerts, Invariant subspaces and invertibility properties for singular systems: The general case, Linear Algebra and Its Applications, 1993, 183: 61-88.
8. F. L. Lewis and K. Ozcaldiran, Geometric structures and feedback in singular systems, IEEE Transactions on Automatic Control, 1989, 34: 450-455.
9. J. J. Loiseau, Some geometric considerations about the Kronecker normal form, International Journal of Control, 1985, 42: 1411-1431.
10. M. Malabre, Generalized linear systems: Geometric and structural approaches, Linear Algebra and its Applications, 1989, 122-123: 591-621.
11. P. Misra, P. Van Dooren, and A. Varga, Computation of structural invariants of generalized state-space systems, Automatica, 1994, 30: 1921-1936.
12. P. Van Dooren, The generalized eigenstructure problem in linear system theory, IEEE Transactions on Automatic Control, 1981, 26: 111-129.
13. P. Van Dooren, The eigenstructure of an arbitrary polynomial matrix: Computational aspects, Linear Algebra and its Applications, 1983, 50: 545-579.
14. G. Verghese, Infinite Frequency Behavior in Generalized Dynamical Systems, PhD Dissertation, Stanford University, 1978.
15. Z. Zhou, M. A. Shayman, and T. J. Tarn, Singular systems: A new approach in the time domain, IEEE Transactions on Automatic Control, 1987, 32: 42-50.
16. ∞ Control, Springer, New York, 2000.
17. 2 Optimal Control, Prentice Hall, London, 1995.
18. M. He and B. M. Chen, Structural decomposition of linear singular systems: The single-input and single-output case, Systems &: Control Letters, 2002, 47: 327-334.
19. P. Sannuti and A. Saberi, A special coordinate basis of multivariable linear systems - Finite and infinite zero structure, squaring down and decoupling, International Journal of Control, 1987, 45: 1655-1704.
20. D. L. Chu, X. Liu, and R. C. E. Tan, On the numerical computation of a structural decomposition in systems and control, IEEE Transactions on Automatic Control, 2002, 47: 1786-1799.
21. B. M. Chen, On the properties of the special coordinate basis of linear systems, International Journal of Control, 1998, 71: 981-1003.
22. Z. Lin, B. M. Chen, and X. Liu, Linear Systems Toolkit. URL: http://www.linearsystemskit.net or http://hdd.ece.nus.edu.sg/~bmchen/linsyskit/ index.html, available online since 2004.