L2-l∞ stability criterion for fixed-point state-space digital filters with saturation nonlinearity

Choon Ki Ahn

doi:10.1080/00207217.2012.743083

L₂-l_∞ stability criterion for fixed-point state-space digital filters with saturation nonlinearity

Choon Ki Ahn^*

^*Corresponding author for this work

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

32 Citations (Scopus)

Abstract

This article proves that there exists an l₂-l_∞ stability criterion for fixed-point state-space digital filters without overflow oscillations. By the l₂-l_∞ stability property, this new criterion guarantees asymptotic stability and attenuates the effect of external interference to a prescribed l₂-l_∞-induced norm bound. We represent this stability criterion as the form of linear matrix inequality, which can be solved easily using the existing numerical packages. Finally, we present an illustrative example, which shows the effectiveness of the proposed stability criterion.

Original language	English
Pages (from-to)	1309-1316
Number of pages	8
Journal	International Journal of Electronics
Volume	100
Issue number	9
DOIs	https://doi.org/10.1080/00207217.2012.743083
Publication status	Published - 2013 Sept 1

Keywords

asymptotic stability
digital filters
finite word length effects
l-l approach
linear matrix inequality

ASJC Scopus subject areas

Electrical and Electronic Engineering

Access to Document

10.1080/00207217.2012.743083

Cite this

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abstract = "This article proves that there exists an l2-l∞ stability criterion for fixed-point state-space digital filters without overflow oscillations. By the l2-l∞ stability property, this new criterion guarantees asymptotic stability and attenuates the effect of external interference to a prescribed l2-l∞-induced norm bound. We represent this stability criterion as the form of linear matrix inequality, which can be solved easily using the existing numerical packages. Finally, we present an illustrative example, which shows the effectiveness of the proposed stability criterion.",

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AB - This article proves that there exists an l2-l∞ stability criterion for fixed-point state-space digital filters without overflow oscillations. By the l2-l∞ stability property, this new criterion guarantees asymptotic stability and attenuates the effect of external interference to a prescribed l2-l∞-induced norm bound. We represent this stability criterion as the form of linear matrix inequality, which can be solved easily using the existing numerical packages. Finally, we present an illustrative example, which shows the effectiveness of the proposed stability criterion.

KW - asymptotic stability

KW - digital filters

KW - finite word length effects

KW - l-l approach

KW - linear matrix inequality

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