In the literature regarding linear systems and mathematical control theory, several different techniques have been developed for obtaining the solution of homogeneous linear time-invariant (LTI) descriptor differential systems. In this article, applying the complex Weierstrass canonical form, we investigate the conditions under which a descriptor system with a specific structure and desired properties is being constructed using perturbation theory. Our approach is very general, and as an example, a stable homogeneous LTI descriptor system is designed. Thus, a proportional and derivative controller can be used, such as the case where a family of perturbed pencils is defined and the solutions of the initial and the relative perturbed systems are rho(M)(t)-close with respect to a Frobenius distance. A Step-algorithm and an illustrative example are also presented to illustrate the results of this article.