Hurwitz stability test of linear systems with commensurate delays

Based on the concepts of Sylvester matrix and Sylvester resultant elimination, sufficient and necessary conditions are developed for the delay-independent stability of a class of delayed systems with commensurate delays, and an effective algorithm is presented for computing the minimal critical value T such that within the delay interval (0, T), the system has the same stability as the one when the delays disappear, if the system is not delay-independent stable. The minimal critical value can be determined simply by computing Sylvester resultant and by solving linear equations.