RELAXATIONS OF ROBUST LINEAR PROGRAMS AND VERIFICATION OF EXACTNESS

Motivated by a robust positive real synthesis problem, we consider robust linear programming problems with the main goal of verifying whether the computed solution of a particular LMI relaxation is exact. It it shown that this requires to solve a polynomial system of equations. The main contribution of this paper is an algorithm to solve polynomial systems. Contrary to existing approaches, we suggest a technique which does not require the computation of a Gröbner basis of the ideal generated by the polynomials that define the equations.