A Note on the Induced l∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{l}}_\infty $$\end{document} Stability of Fixed-Point Digital Filters Without Overflow Oscillations and Instability Due to Finite Wordlength Effects

A recently reported criterion due to Ahn and Lee (Adv Differ Equ 51:1–7, 2012) for the induced l∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{l}}_\infty $$\end{document} stability of fixed-point digital filters without overflow oscillations and instability due to finite wordlength effects is reviewed. This article points out that there is a technical error in the main result and at the same time presents an approach to correcting the main result. Moreover, a relaxed version of the criterion is made available. Illustrative examples are given to demonstrate the effectiveness of the proposed result.