Abstract
In [1], Mertzios introduced two-dimensional (2-D) Lyapunov equations for the covariance and noise matrices to analyze the output roundoff noise under l_{2} -norm scaling in 2-D digital filters described by the local state-space model. However, his 2-D Lyapunov equations include some crucial errors. This paper presents a counterexample to his 2-D Lyapunov equations, and shows that his 2-D Lyapunov equations cannot give the covariance and noise matrices in 2-D state-space digital filters.
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