A new method is presented for determining delay-independent stability zones of the general LTI dynamics with multiple delays against parametric uncertainties. This method utilizes extended kronecker summation and unique properties of self-inversive polynomials. Self-inversive polynomials are special polynomials which exert useful tools for examination of the distribution of its zeros. A sufficient condition for delay-independent stability is presented. The main foci in this paper is a novel approach to the robustness of the time-delayed systems. A new sufficient condition for delay-independent stability is introduced. These new concepts are also demonstrated via some example case studies.