Solution of Lyapunov equation for the state matrix

A spectral method for the solution of the Lyapunov equation for the state matrix A is described if the symmetric matrices P and Q are known. This can be used to ‘identify’ the matrix A if P is obtained as a Grammian matrix. The solution has a symmetric component and an arbitrary skew-symmetric component in a transformed domain. Bounds on the real parts of the eigenvalues of A are also obtained.