Solutions of Higher Order Homogeneous Linear Matrix Differential Equations For Consistent and Non Consistent Initial Conditions

Solving Higher Order Homogeneous Linear Matrix Differential Equations

Abstract

In this article, we study a class of linear matrix differetialequations (regular case) of higher order whose coefficients are square constant matrices.By using matrix penciltheory and the Weierstrass cannonical form of the pencilwe obtain formulas for the solutions and we show that the solution is unique for consistent initial conditions and infinite fornon-consistent initial conditions.Moreover we provide some numerical examples.These kinds of systems are inherent in many physical and engineering phenomena.