Closed Forms of General Solutions for Rectangular Systems of Coupled Generalized Sylvester Matrix Differential Equations

Pattrawut Chansangiam


We investigate a rectangular system of coupled generalized Sylvester matrix differential equations in both nonhomogeneous and homogeneous cases. In order to obtain a closed form of its general solution, we transform it to an equivalent vector differential equation. This is done by using the vector operator and the Kronecker product. An explicit form of its general solution is given in terms of matrix series concerning Mittag-Leffler functions, exponentials, and hyperbolic functions. The main system includes certain systems of coupled matrix/vector differential equations, and single matrix differential equations as special cases.


Matrix differential equation; Vector operator; Kronecker product; Mittag-Leffler function; Matrix exponential

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