Solutions of Higher-Order Homogeneous Linear Matrix Differential Equations for Consistent and Non-Consistent Initial Conditions : Regular Case

الملخص EN

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 we show that the solution is 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.