Abstract: The stability radius problem of Hurwitz polynonmials with respect to the Holder p-norm-bounded uncertainties in the coefficients is considered .Usually,the solution to the stability radius problem demands the computation of the infimum of some certain functions, and can be approached only numerically Using root locus technique, these functions are analysed and it is shown that, in some spedal cases , the infimum can be achieved only at some non-stationary points which can be specified previously , hence, analytical solutions to the stability radius problem are available.