Strict dissipativity and asymptotic stability of digital filters in direct form with saturation nonlinearity

Choon Ki Ahn, Peng Shi

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this paper, we investigate the strict dissipativity and asymptotic stability of digital filters in the direct form with saturation nonlinearity. First, a novel criterion is presented for the (Q, S, R)-(Formula presented.)-dissipativity of single digital filters in the direct form. By selecting the weighting scalar parameters, this condition reduces to the conditions for (Formula presented.), passivity, and mixed (Formula presented.)/passivity performances. Based on this result, a new sufficient criterion is proposed for the (Q, S, R)-(Formula presented.)-dissipativity of interconnected digital filters in the direct form. A condition for the asymptotic stability of interconnected direct-form digital filters is also presented, and three numerical examples are included to show the effectiveness of the developed theoretical results.

Original languageEnglish
Pages (from-to)1-9
Number of pages9
JournalNonlinear Dynamics
DOIs
Publication statusAccepted/In press - 2016 Mar 7

Fingerprint

Dissipativity
Digital Filter
Digital filters
Asymptotic stability
Asymptotic Stability
Saturation
Nonlinearity
Passivity
Weighting
Scalar
Sufficient
Numerical Examples
Form

Keywords

  • Digital filter
  • Direct form
  • Dissipativity
  • Interconnection
  • Stability

ASJC Scopus subject areas

  • Applied Mathematics
  • Mechanical Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Electrical and Electronic Engineering
  • Control and Systems Engineering

Cite this

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abstract = "In this paper, we investigate the strict dissipativity and asymptotic stability of digital filters in the direct form with saturation nonlinearity. First, a novel criterion is presented for the (Q, S, R)-(Formula presented.)-dissipativity of single digital filters in the direct form. By selecting the weighting scalar parameters, this condition reduces to the conditions for (Formula presented.), passivity, and mixed (Formula presented.)/passivity performances. Based on this result, a new sufficient criterion is proposed for the (Q, S, R)-(Formula presented.)-dissipativity of interconnected digital filters in the direct form. A condition for the asymptotic stability of interconnected direct-form digital filters is also presented, and three numerical examples are included to show the effectiveness of the developed theoretical results.",
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