A Computational Method for Determining Strong Stabilizability of n-D Systems

Journal of Symbolic Computation

Volumn 27, Issue 5, 1999, Pages 479-499

  Ying, Jiang Qian ^a   Xu, Li ^b   Lin, Zhiping ^c  

^a GIFU UNIVERSITY   (Japan)

^b ASAHI UNIVERSITY   (Japan)

^c NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001496305     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsco.1999.0263     Document Type: Article

References (28)

1. Anderson B. D. O., Bose N. K., Jury E. I. Output feedback stabilization and related problems - solution via decision methods. IEEE Trans. Autom. Control. 20:1975;53-66.
2. Arnon D., Collins G., McCallum S. Cylindrical algebraic decomposition I, II. SIAM J. Comput. 13:1984;865-889.
3. Blondel V., Gevers M. Simultaneous stabilization of three linear systems is rationally undecidable. Math. Control Signals Syst. 6:1994;135-145.
4. Blondel V., Tsitsiklis J. N. NP-hardness of some linear control design problems. SIAM J. Control Optim. 35:1997;2118-2127.
5. Bose N. K. Special issue on multidimensional systems. Proc. IEEE. 65:1977;819-980.
6. Bose N. K. Applied Multidimensional Systems Theory. 1982;Van Nostrand Reinhold, New York.
7. Bose N. K. Multidimensional System Theory. 1985;Reidel, Dordrecht.
8. Bose N. K., Modarressi A. R. General procedure for multivariable polynomial positivity test with control applications. IEEE Trans. Autom. Control. 21:1976;696-701.
9. Buchberger B. Gröbner bases: an algorithmic method in polynomial ideal theory. Bose N. K. Multidimensional System Theory. 1985;184-232 Reidel, Dordrecht.
10. Buchberger B., Loos R. Algebraic simplification. Buchberger B., Collins G. E., Loos R. Computer Algebra - Symbolic and Algebraic Computation. 1982;11-44 Springer-Verlag, Wien.
11. Collins G. Quantifier Elimination for Real Closed Fields by Cylindrical Algebraic Decomposition. 33:1975;. p. 134-183.
12. Collins G., Hong H. Partial cylindrical algebraic decomposition and quantifier elimination. J. Symb. Comput. 12:1991;299-328.
13. Cooke G., Finney R. Homology of Cell Complexes. 1967;Princeton University Press, Princeton.
14. Dorato P., Yang W., Abdallah C. Robust multi-objective feedback design by quantifier elimination. J. Symb. Comput. 24:1997;153-159.
15. Foulds L. R. Graph Theory Applications. 1992;Springer-Verlag, New York.
16. Fulton W. Algebraic Topology - A First Course. 1995;Springer-Verlag, Berlin.
17. Hong H., Liska R., Steinberg S. Testing stability by quantifier elimination. J. Symb. Comput. 24:1997;161-187.
18. Jirstrand M. Nonlinear control system design by quantifier elimination. J. Symb. Comput. 24:1997;137-152.
19. Jury E. Stability of multidimensional scalar and matrix polynomials. Proc. IEEE. 66:1978;1018-1047.
20. Lin Z. Feedback stabilizability of mimo n-d linear systems. Multidimens. Syst. Signal Process. 9:1998;149-172.
21. Schwartz J. T., Sharir M. On the piano mover's problem II: general techniques for computing topological properties of real algebraic manifolds. Adv. Appl. Math. 4:1983;298-351.
22. Shankar S. An obstruction to the simultaneous stabilization of two n-D plants. Acta Appl. Math. 36:1994;289-301.
23. Shankar S., Sule V. R. Algebraic geometric aspects of feedback stabilization. SIAM J. Control Optim. 30:1992;11-30.
24. Vidyasagar M. Control System Synthesis - A Factorization Approach. 1985;MIT Press, Cambridge.
25. Weispfenning V. Simulation and optimization by quantifier elimination. J. Symb. Comput. 24:1997;189-208.
26. Xu L., Saito O., Abe K. Output feedback stabilizability and stabilization algorithms for 2D systems. Multidimens. Syst. Signal Process. 5:1994;41-60.
27. Ying J. Q. Conditions for strong stabilizabilities of n-dimensional systems. Multidimens. Syst. Signal Process. 9:1998;125-148.
28. Youla D. C., Bongiorno J. J., Lu C. N. Single loop feedback stabilization of linear multivariable plants. Automatica. 10:1974;159-173.