SyNRAC: A Maple-Package for Solving Real Algebraic Constraints

In this paper we present a maple-package, named SyNRAC, for solving real algebraic constraints derived from various engineering problems. Our main tool is real quantifier elimination and we focus on its application to robust control design problems.

[1]  M. Jirstrand Constructive Methods for Inequality Constraints in Control , 1998 .

[2]  H. Yanami,et al.  A Matlab toolbox for robust control synthesis by symbolic computation , 2004, SICE 2004 Annual Conference.

[3]  George E. Collins,et al.  Quantifier elimination for real closed fields by cylindrical algebraic decomposition , 1975 .

[4]  S. Hara,et al.  Fixed-structure robust controller synthesis based on sign definite condition by a special quantifier elimination , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[5]  George E. Collins,et al.  Partial Cylindrical Algebraic Decomposition for Quantifier Elimination , 1991, J. Symb. Comput..

[6]  L. González-Vega A Combinatorial Algorithm Solving Some Quantifier Elimination Problems , 1998 .

[7]  B. F. Caviness,et al.  Quantifier Elimination and Cylindrical Algebraic Decomposition , 2004, Texts and Monographs in Symbolic Computation.

[8]  Rüdiger Loos,et al.  Applying Linear Quantifier Elimination , 1993, Comput. J..

[9]  Hirokazu Anai,et al.  A Parameter Space Approach for Fixed-order robust controller synthesis by symbolic computation (Computer Algebra : Algorithms, Implementations and Applications) , 2002 .

[10]  Tomás Recio,et al.  Sturm-Habicht sequence , 1989, ISSAC '89.

[11]  D. Siljak New algebraic criteria for positive realness , 1971 .

[12]  Shinji Hara,et al.  Parameter Space Design for H∞ Control , 1991 .

[13]  Thomas Sturm,et al.  Real Quantifier Elimination in Practice , 1997, Algorithmic Algebra and Number Theory.

[14]  Volker Weispfenning,et al.  The Complexity of Linear Problems in Fields , 1988, Journal of symbolic computation.

[15]  Wei Yang,et al.  Robust Multi-Objective Feedback Design by Quantifier Elimination , 1997, J. Symb. Comput..

[16]  Tetsuya Kimura,et al.  A Robust Control System Design by a Parameter Space Approach Based on Sign Definite Condition , 1991 .

[17]  H. Anai,et al.  On solving semidefinite programming by quantifier elimination , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[18]  Hirokazu Anai,et al.  SyNRAC: a maple-package for solving real algebraic constraints toward a robust parametric control toolbox , 2003, SICE 2003 Annual Conference (IEEE Cat. No.03TH8734).

[19]  George E. Collins,et al.  Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition , 1975, Automata Theory and Formal Languages.

[20]  Thomas Sturm,et al.  Simplification of Quantifier-Free Formulae over Ordered Fields , 1997, J. Symb. Comput..

[21]  S. Hara,et al.  Linear programming approach to robust controller design by a quantifier elimination , 2002, Proceedings of the 41st SICE Annual Conference. SICE 2002..

[22]  Shankar P. Bhattacharyya,et al.  Robust control under parametric uncertainty. Part II: design , 1999 .

[23]  Volker Weispfenning,et al.  Quantifier Elimination for Real Algebra — the Quadratic Case and Beyond , 1997, Applicable Algebra in Engineering, Communication and Computing.

[24]  Marie-Françoise Roy,et al.  Sturm—Habicht Sequences, Determinants and Real Roots of Univariate Polynomials , 1998 .