Stability of a real polynomial set with coefficients in a weighted L/sub p/ domain

摘要

N.K. Bose and K.D. Kim (1989) attempted to show that the strict Hurwitz property of a family of polynomials having real coefficients in a L/sub p/ domain for a fixed integer p in (1, infinity ) 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/sub p/ domain for a fixed real p in (0, infinity ) are derived. The results of Kharitonov are obtained as a special case of p= infinity .