Skip to main content
SpringerLink
Log in

Bounded Real Lemma for 2-D Discrete Systems Using Asymmetric Lyapunov Matrix: What Shall It Be?

  • Short Paper
  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

In this paper, we examine a recently reported bounded real lemma for two-dimensional (2-D) discrete systems using asymmetric Lyapunov matrix (Vidyarthi et al. in Circuits Syst Signal Process 36(10):3901–3918, 2017). It is shown that the bounded real lemma, as it is, is incorrect and may lead to erroneous conclusion. Moreover, various corrected and equivalent forms of their bounded real lemma are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N. Agarwal, H. Kar, A note on stability analysis of 2-D linear discrete systems based on the Fornasini–Marchesini second model: Stability with asymmetric Lyapunov matrix. Digit. Signal Process. 37, 109–112 (2015)

    Article  Google Scholar 

  2. C. Du, L. Xie, Y.C. Soh, \(H_\infty \) filtering of 2-D discrete systems. IEEE Trans. Signal Process. 48(6), 1760–1768 (2000)

    Article  MATH  Google Scholar 

  3. E. Fornasini, G. Marchesini, Doubly-indexed dynamical systems: state-space models and structural properties. Math. Syst. Theory 12(1), 59–72 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  4. T. Hinamoto, Stability of 2-D discrete systems described by the Fornasini–Marchesini second model. IEEE Trans. Circuits Syst. I 44(3), 254–257 (1997)

    Article  MathSciNet  Google Scholar 

  5. W.-S. Lu, On a Lyapunov approach to stability analysis of 2-D digital filters. IEEE Trans. Circuits Syst. I 41(10), 665–669 (1994)

    Article  Google Scholar 

  6. V. Singh, Stability analysis of 2-D linear discrete systems based on the Fornasini–Marchesini second model: stability with asymmetric Lyapunov matrix. Digit. Signal Process. 26, 183–186 (2014)

    Article  Google Scholar 

  7. A. Vidyarthi, M. Tiwari, A. Dhawan, Robust optimal \(H_\infty \) control for 2-D discrete systems using asymmetric Lyapunov matrix. Circuits Syst. Signal Process. 36(10), 3901–3918 (2017)

    Article  MATH  Google Scholar 

  8. L. Xie, C. Du, Y.C. Soh, C. Zhang, \(H_\infty \) and robust control of 2-D systems in FM second model. Multidimens. Syst. Signal Process. 13(3), 265–287 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  9. L. Xie, C. Du, C. Zhang, Y.C. Soh, \(H_\infty \) deconvolution filtering of 2-D digital systems. IEEE Trans. Signal Process. 50(9), 2319–2332 (2002)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electronics and Communication Engineering, Motilal Nehru National Institute of Technology Allahabad, Allahabad, 211004, India

    Neha Agarwal & Haranath Kar

Authors
  1. Neha Agarwal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Haranath Kar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Neha Agarwal.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Agarwal, N., Kar, H. Bounded Real Lemma for 2-D Discrete Systems Using Asymmetric Lyapunov Matrix: What Shall It Be?. Circuits Syst Signal Process 37, 4082–4089 (2018). https://doi.org/10.1007/s00034-018-0749-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-018-0749-0

Keywords

Search

Navigation