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Simultaneous Stabilizability of 3 Linear-systems Is Rationally Undecidable

Bibliographic reference Blondel, Vincent ; Gevers, Michel. Simultaneous Stabilizability of 3 Linear-systems Is Rationally Undecidable. In: Mathematics of Control, Signals and Systems, Vol. 6, no. 2, p. 135-145 (1993)
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  1. B. D. O. Anderson, A note on the Youla-Bongiorno-Lu condition,Automatica,2 (1976), 387?388.
  2. A. Baker,Transcendental Number Theory, revised edn., Cambridge University Press, Cambridge, 1979.
  3. A. Bermant, Dilatation d'une fonction modulaire et problémes de recouvrement,Mat. Sb.,15 (1944), 285?324.
  4. V. Blondel, Simultaneous Stabilization: Mathematical Solutions, Related Problems and Equivalent Formulations, Ph.D. Thesis, University of Louvain, May 1992.
  5. V. Blondel, G. Campion, and M. Gevers, Avoidance and intersection in the complex plane, a tool for simultaneous stabilization,Proceedings of the 30th IEEE Conference on Decision and Control, Brighton, 1991, pp. 285?290.
  6. V. Blondel, M. Gevers, R. Mortini, and R. Rupp, Simultaneous stabilization of three or more plants: conditions on the real axis do not suffice, Preprint, 1991; to appear inSIAM J. Control Optim.
  7. B. Ghosh, Some new results on the simultaneous stabilizability of a family of single-input single-output systems,Systems Control Lett.,6 (1985), 39?45.
  8. B. Ghosh, Transcendental and interpolation methods in simultaneous stabilization and simultaneous partial pole placement problems,SIAM J. Control Optim.,24 (1986), 1091?1109.
  9. G. Goluzin,Geometric Theory of Functions of a Complex Variable, Translations of Mathematical Monographs, Vol. 26, American Mathematical Society, Providence, RI, 1969.
  10. H. Kwakernaak, A condition for robust stabilizability,Systems Control Lett.,2 (1985), 1005?1013.
  11. Z. Nehari,Conformal Mapping, McGraw-Hill, New York, 1952 (reprinted by Dover, New York, 1975).
  12. W. Rudin,Real and Complex Analysis, 3rd edn., McGraw-Hill, New York, 1987.
  13. R. Saeks and J. Murray, Fractional representation, algebraic geometry and the simultaneous stabilization problem,IEEE Trans. Automat. Control,27 (1982), 895?903.
  14. M. Vidyasagar,Control System Synthesis: A Factorization Approach, MIT Press, Cambridge, MA, 1985.
  15. M. Vidyasagar and N. Viswanadham, Algebraic design techniques for reliable stabilization,IEEE Trans. Automat. Control,27 (1982), 1085?1095.
  16. K. Wei, The Solution of a Transcendental Problem and Its Application in Simultaneous Stabilization Problems, DLR Technical Report, Reference R38-91, 1991.
  17. K. Wei and B. R. Barmish, An iterative design procedure for simultaneous stabilization of MIMO systems,Automatica,24 (1988), 643?652.
  18. D. Youla, J. Bongiorno, and C. Lu, Single-loop feedback stabilization of linear multivariable plants,Automatica,10 (1974), 159?173.