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Differential equations of the form A x + Bx = f are studied where A, B are m × n matrices. Explicit solutions are derived for several cases of interest. One such case is when there exists a scalar λ such that λ A + B is of full rank. Another includes the case when A, B are normal matrices and one is positive semidefinite. The application of these results to linear autonomous control processes is discussed.
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Stephen L. Campbell (1977) studied this question.
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