Engineering Analysis/Lyapunov Equation

$AM+MB=C$

Where A, B and C are constant square matrices, and M is the solution that we are trying to find. If A, B, and C are of the same order, and if A and B have no eigenvalues in common, then the solution can be given in terms of matrix exponentials:

$M=-\underset{0}{\overset{\mathrm{\infty }}{\int }}{e}^{Ax}C{e}^{Bx}dx$