Solutions of higher-order homogeneous linear matrix differential equations for consistent and non-consistent initial conditions: regular case (Q642818)

Summary: We study a class of linear matrix differential equations (regular case) of higher order whose coefficients are square constant matrices. By using matrix pencil theory and the Weierstrass canonical form of the pencil, we obtain formulas for the solutions and show that these solutions are unique for consistent initial conditions and infinite for nonconsistent initial conditions. Moreover, we provide some numerical examples. These kinds of systems are inherent in many physical and engineering phenomena.