On the solution of higher order homogeneous complex linear descriptor differential systems with symmetric/skew-symmetric coefficients

This paper introduces the results of Thompson's canonical form under congruence for pairs of complex matrices with symmetric and skew symmetric structural properties to the solution of higher order linear homogeneous dynamic systems. Under this approach, the main equation is divided into several sub-systems whose solutions are derived. Note that the regularity or singularity of matrix pencil pre-determines the number of sub-systems. The special properties of such systems may be appeared in engineering and even in some financial models.