Robust performance and structured singular value computation by quantifier elimination

We consider the problem of computing the robust performance norm in H^∞ or equivalently, the complex structured singular value. This problem is equivalent to that of computing the H^∞ norm of a function of several complex variables. We show how one can use quantifier elimination techniques to provide a test for whether the H^∞ norm is less than one. These techniques can be viewed as a generalization of the use of Sturm´s theorem to compute H ^∞ norms in the one variable case