On the frequency dependent Lyapunov equation

A frequency dependent Lyapunov equation was recently used in the stability analysis of two-dimensional (2-D) digital systems, but no general solution was developed. In this paper a general form of the frequency dependent Lyapunov matrix is proposed and a set of equations which completely characterize the solution are derived. Applications of the results to the evaluation of quantization error in 2-D filters is also outlined.