The physical parameters of controlled systems (plants) are uncertain and are accompanied by nonlinearity. The state space equation and the characteristic polynomial of the control system should, therefore, be expressed by an interval set of parameters. This paper examines the robust performance evaluation of that type of control system based on the existing area of characteristic roots (i.e., eigenvalues). In particular, in this paper, a sufficient condition for the roots area which is enclosed by a specified circle on a complex variable plane is given by applying the classic Sturm’s theorem (division algorithm) to the four corners of a segment polynomial. The result that is obtained by finite calculations in regard to the coefficients of the segment polynomial, can be extended to general interval polynomials with multiple uncertain parameters.