Linear Systems of Differential Equations with Singular Coefficients

Abstract

Differential equations of the form $A\dot x + Bx = f$ are studied where A, B are $m \times n$ matrices. Explicit solutions are derived for several cases of interest. One such case is when there exists a scalar $\lambda $ such that $\lambda A + B$ 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.