Notes on matrix theory. X. A problem in control

Abstract

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