Solving systems of polynomial inequalities with algebraic geometry methods

TL;DR

This paper introduces computational algebraic geometry methods to solve systems of polynomial inequalities, reformulating inequalities as equations and applying three solution techniques, demonstrated on control system stabilization problems.

Contribution

It presents new computational tools and adapts existing algebraic geometry methods to efficiently solve polynomial inequality systems.

Findings

Successfully reformulated inequalities as polynomial equations

Proposed three methods for solving polynomial systems

Applied methods to control system stabilization problem

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.