Feedback stabilizability of MIMO n-D linear systems

Multidimensional Systems and Signal Processing

Volumn 9, Issue 2, 1998, Pages 149-172

  Lin, Zhiping ^a  

^a DSO NATIONAL LABORATORIES   (Singapore)

Author keywords

Generating polynomials; Matrix fraction description; n D System; Output feedback; Polynomial matrices; Stabilizability

Indexed keywords

FEEDBACK CONTROL; LINEAR CONTROL SYSTEMS; MATRIX ALGEBRA; POLYNOMIALS;

DIMENSIONAL LINEAR SYSTEMS; MATRIX FRACTION DESCRIPTIONS; MULTI INPUT MULTI OUTPUT SYSTEMS;

SYSTEM STABILITY;

EID: 0032048448     PISSN: 09236082     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008230204251     Document Type: Article

References (20)

1. C. A. Desoer, R.-W. Liu, J. Murray, and R. Saeks, "Feedback System Design: The Fractional Representation Approach to Analysis and Synthesis," IEEE Trans Automat. Contr., vol. 25, 1980, pp. 399-412.
2. M. Vidyasagar, H. Schneider, and B. A. Francis, "Algebraic and Topological Aspects of Feedback Stabilization," IEEE Trans Automat. Contr., vol. 27, 1982, pp. 880-894.
3. M. Vidyasagar, Control System Synthesis: A Factorization Approach, Cambridge, MA: MIT Press, 1985.
4. J. P. Guiver and N. K. Bose, "Causal and Weakly Causal 2-D Filters with Applications in Stabilizations," in Multidimensional Systems Theory: Progress, Directions and Open Problems (N. K. Bose, ed.), Dordrecht: Reidel, 1985, p. 52.
5. M. Bisiacco, E. Fornasini, and G. Marchesini, "Controller Design for 2D Systems," in Frequency Domain and State Space Methods for Linear Systems, (C. I. Byrnes and A. Lindquist, eds.), North-Holland: Elsevier, 1986, pp. 99-113.
6. Z. Lin, "Feedback Stabilization of Multivariable Two-Dimensional Linear Systems," Int. J. Contr., vol. 48, 1988, pp. 1301-1317.
7. L. Xu, O. Saito, and K. Abe, "Output Feedback Stabilizability and Stabilization Algorithms for 2-D Systems," Mutidimensional Systems and Signal Processing, vol. 5, 1994, pp. 41-60.
8. V. R. Sule, "Feedback Stabilization Over Commutative Rings: The Matrix Case," SIAM J. Contr. Optim., vol. 32, 1994, pp. 1675-1695.
9. E. I. Jury, "Stability of Multidimensional Systems and Related Problems," in Multidimensional Systems: Techniques and Applications (S. G. Tzafestas, ed.), New York: Marcel Dekker, 1986, p. 89.
10. N. K. Bose, Applied Multidimensional Systems Theory. New York: Van Nostrand Reinhold, 1982.
11. D. C. Youla and G. Gnavi, "Notes on n-Dimensional System Yheory," IEEE Trans. Circuits Syst., vol. 26, 1979, pp. 105-111.
12. D. C. Youla and P. F. Pickel, "The Quillen-Suslin Theorem and the Structure of n-Dimensional Elementary Polynomial Matrices," IEEE Trans. Circuits Syst., vol. 31, 1984, pp. 513-518.
13. Z. Lin, "On Matrix Fraction Descriptions of Multivariable Linear n-D Systems," IEEE Trans. Circuits Syst., vol. 35, 1988, pp. 1317-1322.
14. Z. Lin, "On Primitive Factorizations for 3-D Polynomial Matrices," IEEE Trans. Circuits Syst., vol. 39, 1992, pp. 1024-1027.
15. S. Shankar and V. R. Sule, "Algebraic Geometric Aspects of Feedback Stabilization," SIAM J. Contr. Optim., vol. 30, 1992, pp. 11-30.
16. C. A. Berenstein and D. C. Struppa, "1-Inverses for Polynomial Matrices of Non-Constant Rank," Systems & Control Letters, vol. 6, 1986, pp. 309-314.
17. F. R. Gantmacher, Theory of Matrices, vol. I and II, New York: Chelsea, 1959.
18. 2]," IEEE Trans Automat. Contr., vol. 30, 1985, pp. 161-162.
19. J. P. Guiver, "The Equation Ax = b over the Ring C[z, w]," in Multidimensional Systems Theory: Progress, Directions and Open Problems (N. K. Bose, ed.), Dordrecht: Reidel, 1985, p. 233.
20. B. Buchberger, "Gröbner Bases: An Algorithmic Method in Polynomial Ideal Theory," in Multidimensional Systems Theory: Progress, Directions and Open Problems (N. K. Bose, ed.), Dordrecht: Reidel, 1985, p. 184.