A direct synthesis ofQin the Lyapunov equationQ = [A'R + RA]

In the application of Lyapunov's second method to linear systems it is shown that a direct synthesis of the
Q
matrix from the system equations (in the expression
Q = -[A'R + RA]
) is possible. Application to the general third-order linear system is made and the results are seen to be identical to the Routh-Hurwitz criteria.