A new robust stability test for linear control systems is described. The condition at which robust stability is violated is transformed into an equivalent problem in which the existence of a real root of a multivariable polynomial is investigated, This multivariable problem is reduced to that of the solvability of a set of univariable polynomial equations in real numbers, for which a number of efficient numerical methods are available, The use of the method is illustrated in the design of feedback control for an open-loop unstable batch chemical reactor.