Solving systems of polynomial inequalities with algebraic geometry   methods
  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. 
Laura Menini, Corrado Possieri and Antonio Tornamb\`e
math.DS math.AG