A Counterexample to 2-D Lyapunov Equations by Mertzios

Tao Lin; Masayuki Kawamata

doi:10.1109/TCS.1985.1085657

A Counterexample to 2-D Lyapunov Equations by Mertzios

Tao Lin, Masayuki Kawamata

ENG - Electronic Engineering

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

In [1], Mertzios introduced two-dimensional (2-D) Lyapunov equations for the covariance and noise matrices to analyze the output roundoff noise under ‘l₂-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.

Original language	English
Pages (from-to)	1310-1311
Number of pages	2
Journal	IEEE transactions on circuits and systems
Volume	32
Issue number	12
DOIs	https://doi.org/10.1109/TCS.1985.1085657
Publication status	Published - 1985 Dec

ASJC Scopus subject areas

Engineering(all)

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abstract = "In [1], Mertzios introduced two-dimensional (2-D) Lyapunov equations for the covariance and noise matrices to analyze the output roundoff noise under {\textquoteleft}l2-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.",

author = "Tao Lin and Masayuki Kawamata",

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AB - In [1], Mertzios introduced two-dimensional (2-D) Lyapunov equations for the covariance and noise matrices to analyze the output roundoff noise under ‘l2-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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