Detecting of zeros locations in a linear differential-difference equation

In this paper a simple method is presented for detecting of zeros location in a linear differential-difference equations with delay by using dominant gain concept and shown that it is much more general and representative than the conventional theory of asymptotic location of zeros. Dominant gain concept states that in a specific frequency band, the dynamic behavior of a quasi-polynomial traces the dynamics of that term in the quasi-polynomial which dominates in its gain with respect to the other term. If it is minimum phase, quasi-polynomial dynamic behavior is minimum phase that means resulting zeros of time delay parameters are in LHP. Also if it is non minimum phase, quasi-polynomial dynamic behavior is non minimum phase that means resulting zeros of time delay parameters are in RHP. This result is very important to design control structure for time delay system.