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arXiv:1603.01183math.DS

Solving systems of polynomial inequalities with algebraic geometry methods

Laura Menini, Corrado Possieri, Antonio Tornambè

Abstract

The goal of this paper is to provide computational tools able to find a solution of a system of polynomial inequalities. The set of inequalities is reformulated as a system of polynomial equations. Three different methods, two of which taken from the literature, are proposed to compute solutions of such a system. An example of how such procedures can be used to solve the static output feedback stabilization problem for a linear parametrically-varying system is reported.

arXiv comments
15 pages, 2 figures
Journal reference
DOI
Subjects
math.DSDynamical Systems math.AGAlgebraic Geometry

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Linked by 2 identifiable commenters in 2 comments across 2 threads, from Jun 2020 to Apr 2023.

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Discussed in comments2 threads

  1. Use Gröbner bases to solve polynomial equations 1 comment

    • It seems that you can reformulate inequalities into equalities and solve the system: https://arxiv.org/pdf/1603.01183.pdf

      ransac9000View on HNParent context

  2. SageMath – Open-Source Mathematical Software System 1 comment

    • > Can Grobner basis techniques be used to solve a set of quadratic inequalities? One application of Gröbner bases is to solve systems of polynomial equations [0], and characterize their solutions. In many circumstances it is not however the best method, for example if you are…

      enriqutoView on HNParent context

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