Perturbation theory for a homogeneous descriptor regular differential system

This paper is concerned with the dynamic response of a general class of linear systems, the right parameter of which undergoes step perturbations. We solve both systems using the Weierstrass Canonical form (powerful tool of matrix pencil theory). After that, we calculate and compare the relationship between the two solutions. This comparison is of considerable importance in numerical analysis since it has a direct bearing upon the accuracy of any particular method used to construct the solution of the base system.