Stability of a real polynomial set with coefficients in a weighted Lp domain

Recently, Bose and Kim [1989] have attempted to show that the strict Hurwitz property of a family of polynomials having real coefficients in a L_p domain for a fixed integer p∈[1,∞) only requires the checking of eight combinations of fixed polynomials to be strictly Hurwitz. While the main result for p=1 is correct, the generalization to p>1 is incorrect. New necessary and sufficient conditions for the stability of a real polynomial set with coefficients in a weighted L_p domain for a fixed real p∈(0,∞) are derived. The results of Kharitonov are obtained as a special case of p=∞