Lyapunov's matrix equation with system matrix in companion form
PAUL F. CURRAN · International Journal of Control · 1993
A simple method for solving Lyapunov's matrix equation for linear continuous systems with the system matrix in companion form is proposed. The method involves the inversion of the Hurwitz matrix. A necessary and sufficient condition for the existence of a solution to the equation is also obtained. This condition applies even in the critical case where the sum of two eigenvalues of the system matrix is zero.