Notes on matrix theory. X. A problem in control

In the theory of control processes, it is important to be able to calculate $\smallint _0^\infty \left ( {x,Bx} \right )dt$ without having to solve explicitly the differential equation $dx/dt = Ax, \\ x\left ( 0 \right ) = c$. A method for doing this is presented in this paper, generalizing one due to Anke for $n$th order linear differential equations.