Representation of solutions to a linear matrix first-order differential equation with delay

Linear matrix delayed differential equation Formula: see text is dealt with, where Formula: see text is a delay, Formula: see text is an independent variable, Formula: see text is an Formula: see text unknown variable matrix, Formula: see text and Formula: see text are given Formula: see text constant matrices, and Formula: see text is a given Formula: see text variable matrix. Under some commutativity conditions, a formula is derived for solving an initial problem Formula: see text, Formula: see text, where Formula: see text is an Formula: see text variable matrix. Previous results are discussed and open problems for further investigations suggested.