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References

 [1]
C. Abdallah, P. Dorato, W. Yang, R. Liska, and S. Steinberg. Applications of quantifier elimination theory to control system design. In 4th IEEE Mediterranean Symposium on Control and Automation, Crete, Greece, 1996.
 [2]
F. Benhamou and F. Goualard. Universally quantified interval constraints. In Proc. of the Sixth Intl. Conf. on Principles and Practice of Constraint Programming (CP'2000), number 1894 in LNCS, Singapore, 2000. Springer Verlag.
 [3]
B. F. Caviness and J. R. Johnson, editors. Quantifier Elimination and Cylindrical Algebraic Decomposition. Springer, 1998.
 [4]
G. E. Collins. Quantifier elimination for the elementary theory of real closed fields by cylindrical algebraic decomposition. In Second GI Conf. Automata Theory and Formal Languages, volume 33 of LNCS, pages 134-183. Springer Verlag, 1975. Also in [3].
 [5]
G. E. Collins and H. Hong. Partial cylindrical algebraic decomposition for quantifier elimination. Journal of Symbolic Computation, 12:299-328, 1991. Also in [3].
 [6]
A. Dolzmann, T. Sturm, and V. Weispfenning. Real quantifier elimination in practice. In B. H. Matzat, G.-M. Greuel, and G. Hiss, editors, Algorithmic Algebra and Number Theory, pages 221-248. Springer, 1998.
 [7]
P. Dorato, W. Yang, and C. Abdallah. Robust multi-objective feedback design by quantifier elimination. Journal of Symbolic Computation, 24:153-159, 1997.
 [8]
P. V. Hentenryck, D. McAllester, and D. Kapur. Solving polynomial systems using a branch and prune approach. SIAM Journal on Numerical Analysis, 34(2), 1997.
 [9]
H. Hong. Non-linear constraints solving over real numbers in constraint logic programming. Technical Report 92-08, RISC-Linz, 1992.
 [10]
H. Hong, R. Liska, and S. Steinberg. Logic, quantifiers, computer algebra and stability. SIAM News, 30(6):10-,13, 1997.
 [11]
H. Hong, R. Liska, and S. Steinberg. Testing stability by quantifier elimination. Journal of Symbolic Computation, 24(2):161-187, 1997.
 [12]
N. I. Ioakimidis. Quantifier elimination in applied mechanics problems with cylindrical algebraic decomposition. International Journal of Solids and Structures, 34(30):4037-4070, 1997.
 [13]
M. Jirstrand. Nonlinear control system design by quantifier elimination. Journal of Symbolic Computation, 24(2):137-152, 1997.
 [14]
M. Jirstrand. Algebraic Methods for Inequality Constraints in Control. PhD thesis, Linköping University, Department of Electrical Engineering, Division of Automatic Control, 1998. No. 527.
 [15]
R. B. Kearfott. Interval computations: Introduction, uses, and resources. Euromath Bulletin, 2(1):95-112, 1996.
 [16]
R. Liska and S. Steinberg. Applying quantifier elimination to stability analysis of difference schemes. Computer Journal, 36(5):497-593, 1993.
 [17]
R. Liska and S. Steinberg. Solving stability problems using quantifier elimination. In R. Jeltsch and M. Mansour, editors, Stability Theory, Proceedings of Conference on Centennial Hurwitz on Stability Theory, pages 205-210, Basel, 1996. Birkhäuser Verlag. International Series of Numerical Mathematics (ISNM) Vol. 121.
 [18]
R. Loos and V. Weispfenning. Applying linear quantifier elimination. The Computer Journal, 36(5):450-462, 1993.
 [19]
R. E. Moore. Interval Analysis. Prentice Hall, Englewood Cliffs, NJ, 1966.
 [20]
A. Neumaier. Interval Methods for Systems of Equations. Cambridge Univ. Press, Cambridge, 1990.
 [21]
S. Ratschan. Continuous first-order constraint satisfaction. In Proceedings of Artificial Intelligence and Symbolic Computation, LNCS. Springer, 2002. To appear, http://www.risc.uni-linz.ac.at/people/sratscha/preprints.html.
 [22]
S. Steinberg and R. Liska. Stability analysis by quantifier elimination. In G. Jacob, N. Ousous, and S. Steinberg, editors, Proceedings SC 93, International IMACS Symposium on Symbolic Computation, New Trends and Developments, pages 62-67, 1993. Lille, France, June 14 - 17, 1993.
 [23]
S. Steinberg and R. Liska. Stability analysis by quantifier elimination. Mathematics and Computers in Simulation, 42(4-6):629-638, 1996.
 [24]
T. Sturm. Reasoning over networks by symbolic methods. Applicable Algebra in Engineering Communication and Computing, 10(1):79-96, September 1999.
 [25]
A. Tarski. A Decision Method for Elementary Algebra and Geometry. Univ. of California Press, Berkeley, 1951. Also in [3].
 [26]
V. Weispfenning. Simulation and optimization by quantifier elimination. Journal of Symbolic Computation, 24(2), 1997.

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