Improved LMI-based criterion for global asymptotic stability of 2-D state-space digital filters described by Roesser model using twoʼs complement arithmetic

https://doi.org/10.1016/j.dsp.2012.01.001Get rights and content

Abstract

An LMI-based criterion for the global asymptotic stability of 2-D state-space digital filters described by the Roesser model employing twoʼs complement overflow arithmetic is presented. Under a certain assumption, the criterion turns out to be an improvement over a criterion due to El-Agizi and Fahmy pertaining to twoʼs complement arithmetic and has a form similar to a criterion due to Xiao and Hill pertaining to saturation arithmetic. Examples show the effectiveness of the new criterion.

Section snippets

Vimal Singh was born in Mirzapur, India, on May 3, 1946. He received the B.Sc. Eng. and M.Sc. Eng. degrees from Banaras Hindu University (BHU), Varanasi, India, in 1969 and 1971, respectively, and the Ph.D. degree from the University of Allahabad, Allahabad, India, in 1976.

He was a Lecturer with BHU from 1971 to 1972. He joined Motilal Nehru National Institute of Technology (MNNIT), Allahabad, as Lecturer in 1972, where he became reader in 1978 and Professor in 1987. He served as Head of

References (41)

  • A. Lepschy et al.

    A contribution to the stability analysis of second-order digital filters with magnitude truncation

    IEEE Trans. Acoust. Speech Signal Process.

    (1987)
  • T. Bose et al.

    Limit cycles in zero input digital filters due to twoʼs complement quantization

    IEEE Trans. Circuits Syst.

    (1990)
  • T. Bose et al.

    Limit cycles due to roundoff in state-space digital filters

    IEEE Trans. Acoust. Speech Signal Process.

    (1990)
  • P. Bauer

    Comments on ‘Limit cycles due to roundoff in state-space digital filters’

    IEEE Trans. Signal Process.

    (1991)
  • T. Bose et al.

    Stability of digital filters implemented with twoʼs complement truncation quantization

    IEEE Trans. Signal Process.

    (1992)
  • R.P. Roesser

    A discrete state-space model for linear image processing

    IEEE Trans. Automat. Control

    (1975)
  • N.G. El-Agizi et al.

    Two-dimensional digital filters with no overflow oscillations

    IEEE Trans. Acoust. Speech Signal Process.

    (1979)
  • D. Liu et al.

    Stability analysis of state-space realizations for two-dimensional filers with overflow non-linearities

    IEEE Trans. Circuits Syst. I

    (1994)
  • H. Kar et al.

    Stability analysis of 2-D digital filters with saturation arithmetic: An LMI approach

    IEEE Trans. Signal Process.

    (2005)
  • V. Singh

    Elimination of overflow oscillations in 2-D digital filters employing saturation arithmetic: An LMI approach

    IEEE Signal Process. Lett.

    (2005)

    • Cited by (0)

    Vimal Singh was born in Mirzapur, India, on May 3, 1946. He received the B.Sc. Eng. and M.Sc. Eng. degrees from Banaras Hindu University (BHU), Varanasi, India, in 1969 and 1971, respectively, and the Ph.D. degree from the University of Allahabad, Allahabad, India, in 1976.

    He was a Lecturer with BHU from 1971 to 1972. He joined Motilal Nehru National Institute of Technology (MNNIT), Allahabad, as Lecturer in 1972, where he became reader in 1978 and Professor in 1987. He served as Head of Electronics Engineering Department at MNNIT from 1996 to 1999. He was a visiting Lecturer at University of Mosul, Mosul, Iraq, and University of Basra, Basra, Iraq, from 1978 to 1979 and from 1981 to 1982, respectively. Since 2002 he is a Professor at Atilim University, Ankara, Turkey. His research interests are in finite wordlength effects in digital signal processing, analog circuits, nonlinear systems, multidimensional systems, stability of neural networks, and model reduction.

    View full text
    Copyright © 2012 Elsevier Inc. All rights reserved.