Skip to main content
SpringerLink
Log in

On Stability Robustness of 2-D Systems Described by the Fornasini–Marchesini Model

  • Published:
Multidimensional Systems and Signal Processing Aims and scope Submit manuscript

Abstract

This paper studies the stability robustness estimates of two-dimensional(2-D) dynamics in the Fornasini–Marchesini model. It isstressed that the use of 2-D Lyapunov matrix inequality is limitedin application to the stability robustness estimate problem.Two alternative ways to estimate the stability robustness ofa 2-D dynamics are proposed. These are applicable in any stable2-D dynamics. The comparison between the stability robustnessestimate by the 2-D Lyapunov matrix inequality and those presentedin this paper is illustrated by a numerical example.

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. E. Fornasini and G. Marchesini, “Stability Analysis of 2-D Systems,” IEEE Trans. Circuit Syst., vol. CAS-27, 1980, pp. 1210–1217.

    Google Scholar 

  2. W.-S. Lu, “On Robust Stability of 2-D Discrete Systems,” IEEE Trans. Automat. Contr., vol. AC-40, 1995, pp. 502–506.

    Google Scholar 

  3. T. Hinamoto, “Stability of 2-D Discrete Systems Described by the Fornasini-Marchesini Second Model,” IEEE Trans. Circuit Syst., vol. CAS-44, 1997, pp. 254–256.

    Google Scholar 

  4. T. Ooba, “On Stability Analysis of 2-D Systems Based on 2-D Lyapunov Matrix Inequalities,” IEEE Trans. Circuit Syst., vol. CAS-47, 2000, pp. 1263–1265.

    Google Scholar 

  5. T. Ooba, “Stabilization of Multidimensional Systems Using Local State Estimators,” Multidimensional Systems and Signal Processing, vol. 12, 2000, pp. 49–61.

    Google Scholar 

  6. T. Hinamoto, “2-D Lyapunov Equation and Filter Design based on the Fornasini-Marchesini Second Model,” IEEE Trans. Circuit Syst., vol. CAS-40, 1993, pp. 102–110.

    Google Scholar 

  7. W.-S. Lu, “On a Lyapunov Approach to Stability Analysis of 2-D Digital Filters,” IEEE Trans. Circuit Syst., vol. CAS-41, 1994, pp. 665–669.

    Google Scholar 

  8. D. Hinrichsen and A. J. Pritchard, “Real and Complex Stability Radii: A Survey,” Progress in Systems and Control Theory, vol. 6, 1990, pp. 119–162.

    Google Scholar 

  9. T. Ooba, “Stability Robustness for Linear State Space Models–ALyapunov Mapping Approach,” Systems & Control Letters, vol. 29, 1997, pp. 191–196.

    Google Scholar 

  10. P. Lancaster and M. Tismenetsky, The Theory of Matrices, Second Edition, Academic, 1985.

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, 466-8555, Japan

    Tatsushi Ooba

Authors
  1. Tatsushi Ooba
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ooba, T. On Stability Robustness of 2-D Systems Described by the Fornasini–Marchesini Model. Multidimensional Systems and Signal Processing 12, 81–88 (2001). https://doi.org/10.1023/A:1008420911857

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1008420911857

Search

Navigation