Solution of Lyapunov equation with system matrix in companion form

A simple method for solving the matrix Lyapunov equation for linear continuous systems with the system matrix in companion form is proposed. If the system is asymptotically stable, the solution of the Lyapunov equation can be obtained directly from the entries of a Routh table. The proposed method does not involve solution of a linear system of equations or matrix inversion and hence is computationally efficient compared to other techniques. It is illustrated by a numerical example