Solving LTI Descriptor (Regular) Differential Multi-Delay Systems Using Matrix Pencil Theory

In this paper, a special class of differential systems, which is known as linear, time invariant (LTI) descriptor (regular) differential systems with multi delays, is analytically studied. These kinds of systems are inherent in many physical, financial, and engineering applications. Using some elements of matrix pencil theory, we decompose the main system into two subsystems, whose solutions are obtained. Moreover, the form of the initial function is given, so the corresponding initial value problem is uniquely solvable, and an illustrative example is presented using Matlab m-file (dde23) based on the explicit Runge-Kutta method.