Local stability analysis and H performance for Lipschitz digital filters with saturation nonlinearity and external interferences

Amina Shams, Muhammad Rehan, Muhammad Tufail, Choon Ki Ahn, Waqas Ahmed

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

This paper proposes a novel method to analyze the local stability of Lipschitz nonlinear digital filtering schemes under saturation overflow nonlinearity. Conditions for the stability analysis and robust performance estimation are provided in the form of matrix inequalities by utilizing Lyapunov theory, local saturation overflow arithmetic, and Lipschitz condition. The proposed criterion ascertains (local) asymptotic stability in the absence of perturbations. Under the effects of external interferences, a condition for the local stability, ensuring the H performance objective, is developed. The proposed approach offers a less conservative and more accurate estimate of H performance index than the global method by utilizing a bound on the interferences energy. Moreover, the proposed criterion, in contrast to the existing global methods, can be employed to choose an adequate word length of a digital hardware for the specified values of tolerable perturbations energy, H performance index, and fixed-point resolution. It is worth mentioning that analysis approaches have not been completely reported in the literature, in which local stability criteria for nonlinear discrete-time filtering prototypes under both overflow and disturbances have been developed. A detailed stability analysis for a nonlinear recurrent neural network is performed for demonstrating the effectiveness of the proposed scheme.

Original languageEnglish
Pages (from-to)101-108
Number of pages8
JournalSignal Processing
Volume153
DOIs
Publication statusPublished - 2018 Dec 1

Fingerprint

Digital filters
Recurrent neural networks
Stability criteria
Asymptotic stability
Hardware

Keywords

  • External interferences
  • H performance
  • Lipschitz digital filters
  • Local stability
  • Saturation overflow

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Electrical and Electronic Engineering

Cite this

Local stability analysis and H performance for Lipschitz digital filters with saturation nonlinearity and external interferences. / Shams, Amina; Rehan, Muhammad; Tufail, Muhammad; Ahn, Choon Ki; Ahmed, Waqas.

In: Signal Processing, Vol. 153, 01.12.2018, p. 101-108.

Research output: Contribution to journalArticle

@article{247fd21891584bc094d81e15cf741541,
title = "Local stability analysis and H∞ performance for Lipschitz digital filters with saturation nonlinearity and external interferences",
abstract = "This paper proposes a novel method to analyze the local stability of Lipschitz nonlinear digital filtering schemes under saturation overflow nonlinearity. Conditions for the stability analysis and robust performance estimation are provided in the form of matrix inequalities by utilizing Lyapunov theory, local saturation overflow arithmetic, and Lipschitz condition. The proposed criterion ascertains (local) asymptotic stability in the absence of perturbations. Under the effects of external interferences, a condition for the local stability, ensuring the H∞ performance objective, is developed. The proposed approach offers a less conservative and more accurate estimate of H∞ performance index than the global method by utilizing a bound on the interferences energy. Moreover, the proposed criterion, in contrast to the existing global methods, can be employed to choose an adequate word length of a digital hardware for the specified values of tolerable perturbations energy, H∞ performance index, and fixed-point resolution. It is worth mentioning that analysis approaches have not been completely reported in the literature, in which local stability criteria for nonlinear discrete-time filtering prototypes under both overflow and disturbances have been developed. A detailed stability analysis for a nonlinear recurrent neural network is performed for demonstrating the effectiveness of the proposed scheme.",
keywords = "External interferences, H performance, Lipschitz digital filters, Local stability, Saturation overflow",
author = "Amina Shams and Muhammad Rehan and Muhammad Tufail and Ahn, {Choon Ki} and Waqas Ahmed",
year = "2018",
month = "12",
day = "1",
doi = "10.1016/j.sigpro.2018.06.026",
language = "English",
volume = "153",
pages = "101--108",
journal = "Signal Processing",
issn = "0165-1684",
publisher = "Elsevier",

}

TY - JOUR

T1 - Local stability analysis and H∞ performance for Lipschitz digital filters with saturation nonlinearity and external interferences

AU - Shams, Amina

AU - Rehan, Muhammad

AU - Tufail, Muhammad

AU - Ahn, Choon Ki

AU - Ahmed, Waqas

PY - 2018/12/1

Y1 - 2018/12/1

N2 - This paper proposes a novel method to analyze the local stability of Lipschitz nonlinear digital filtering schemes under saturation overflow nonlinearity. Conditions for the stability analysis and robust performance estimation are provided in the form of matrix inequalities by utilizing Lyapunov theory, local saturation overflow arithmetic, and Lipschitz condition. The proposed criterion ascertains (local) asymptotic stability in the absence of perturbations. Under the effects of external interferences, a condition for the local stability, ensuring the H∞ performance objective, is developed. The proposed approach offers a less conservative and more accurate estimate of H∞ performance index than the global method by utilizing a bound on the interferences energy. Moreover, the proposed criterion, in contrast to the existing global methods, can be employed to choose an adequate word length of a digital hardware for the specified values of tolerable perturbations energy, H∞ performance index, and fixed-point resolution. It is worth mentioning that analysis approaches have not been completely reported in the literature, in which local stability criteria for nonlinear discrete-time filtering prototypes under both overflow and disturbances have been developed. A detailed stability analysis for a nonlinear recurrent neural network is performed for demonstrating the effectiveness of the proposed scheme.

AB - This paper proposes a novel method to analyze the local stability of Lipschitz nonlinear digital filtering schemes under saturation overflow nonlinearity. Conditions for the stability analysis and robust performance estimation are provided in the form of matrix inequalities by utilizing Lyapunov theory, local saturation overflow arithmetic, and Lipschitz condition. The proposed criterion ascertains (local) asymptotic stability in the absence of perturbations. Under the effects of external interferences, a condition for the local stability, ensuring the H∞ performance objective, is developed. The proposed approach offers a less conservative and more accurate estimate of H∞ performance index than the global method by utilizing a bound on the interferences energy. Moreover, the proposed criterion, in contrast to the existing global methods, can be employed to choose an adequate word length of a digital hardware for the specified values of tolerable perturbations energy, H∞ performance index, and fixed-point resolution. It is worth mentioning that analysis approaches have not been completely reported in the literature, in which local stability criteria for nonlinear discrete-time filtering prototypes under both overflow and disturbances have been developed. A detailed stability analysis for a nonlinear recurrent neural network is performed for demonstrating the effectiveness of the proposed scheme.

KW - External interferences

KW - H performance

KW - Lipschitz digital filters

KW - Local stability

KW - Saturation overflow

UR - http://www.scopus.com/inward/record.url?scp=85050151124&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85050151124&partnerID=8YFLogxK

U2 - 10.1016/j.sigpro.2018.06.026

DO - 10.1016/j.sigpro.2018.06.026

M3 - Article

AN - SCOPUS:85050151124

VL - 153

SP - 101

EP - 108

JO - Signal Processing

JF - Signal Processing

SN - 0165-1684

ER -