Advertisement

H Model Reduction of 2-D Singular Roesser Models

  • Huiling Xu
  • Yun Zou
  • Shengyuan Xu
  • James Lam
  • Qing Wang
Article

Abstract

This paper discusses the problem of H model reduction for linear discrete time 2-D singular Roesser models (2-D SRM). A condition for bounded realness is established for 2-D SRM in terms of linear matrix inequalities (LMIs). Based on this, a sufficient condition for the solvability of the H model reduction problem is obtained via a group of LMIs and a set of coupling non-convex rank constraints. An explicit parameterization of the desired reduced-order models is presented. Particularly, a simple LMI condition without rank constraints is proposed for the zeroth-order H approximation problem. Finally, a numerical example is given to illustrate the applicability of the proposed approach.

Keywords

2-D singular systems H model reduction bounded realness linear matrix inequality Roesser models 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Zhou, K., Li, Y., Lee, EB. 1993“Model Reduction 2-D Systems with Frequency Error Bounds”IEEE Transactions on Circuits and Systems, II.40107110Google Scholar
  2. 2.
    Kando, H., Watanabe, T., Vkai, H., Morita, Y. 1998“A Model Reduction Method of 2D Systems”International Journal of System and Science.299891005Google Scholar
  3. 3.
    Luo, H., Lu, WS., Antoniou, A. 1995“A Weighted Balanced Approximation for 2-D Discrete Systems and its Application to Model Reduction”IEEE Transactions on Circuits and Systems, II.42419429Google Scholar
  4. 4.
    Du, C., Xie, L., Soh, YC. 2001H Reduced Order Approximation of 2-D Digital Filters”IEEE Transactions on Circuits and Systems-I.48688698Google Scholar
  5. 5.
    Xu, S., Lam, J. 2003H Model Reduction for Discrete-Time Singular Systems”Systems and Control Letters.48121133Google Scholar
  6. 6.
    Kaczorek, T. 1988“Singular General Model of 2-D Systems and its Solutions”IEEE Transactions on Automatic Controls.3310611091Google Scholar
  7. 7.
    Kaczorek, T. 1990“General Response Formula and Minimums Energy Control for the General Singular Model for 2-D systems”IEEE Transactions on Automatic Control.35433436Google Scholar
  8. 8.
    Karamanciogle, AV., Lewis, FL. 1992“Geometric Theory for Singular Roesser Model”IEEE Transactions on Automatic Control.37801806Google Scholar
  9. 9.
    Kaczorek, T. 1993“Acceptable Input Sequences for Singular 2-D Linear Systems”IEEE Transactions on Automatic Control.3813911394Google Scholar
  10. 10.
    Zou, Y., Campbell, SL. 2000“The Jump Behavior and Stability Analysis for 2-D Singular Systems”Multidimensional Systems and Signal Processing.11321338Google Scholar
  11. 11.
    Cai, C., Wang, W., Zou, Y. 2004“A Note on the Internal Stability for 2-D Acceptable Linear Singular Discrete Systems”Multidimensional Systems and Signal Processing.15197204Google Scholar
  12. 12.
    Zou Y., Wang W., Xu S. “Structural Stability of 2-D Singular Systems-Part I: Basic Properties”, (2003) International Conference on Control and Automation, Montreal, Canada, June 9–14, 2003Google Scholar
  13. 13.
    Zou Y., Wang W., Xu S. “Structural Stability of 2-D Singular Systems Part II: A Lyapunov Approach”, (2003) International Conference on Control and Automation, Montreal, Canada, June 9–14, (2003)Google Scholar
  14. 14.
    Wang, W., Zou, Y. 2002“The Detectability and Observer Design of 2-D Singular Systems”IEEE Transactions Circuits and Systems.49698703MathSciNetGoogle Scholar
  15. 15.
    Zou Y., Wang W., Xu S. “Regular State Observers Design for 2-D Singular Roesser Models”, (2003) International Conference on Control and Automation, Montreal, Canada, June 9–14, 2003Google Scholar
  16. 16.
    Kaczorek, T. 1989“The Linear-quadratic Optimal Regulator for Singular 2-D Systems with Variable Coefficients”IEEE Transactions on Automatic Control.34565566Google Scholar
  17. 17.
    Xu, H., Zou, Y., Xu, S., Lam, J. 2005“Bounded Real Lemma and Robust H Control of 2-D Singular Roesser Models”Systems and ontrol Letters.54339346Google Scholar
  18. 18.
    Iwasaki, T., Skelton, RE. 1994“All Controllers for the General H Control Problem: LMI Existence Conditions and State Space Formulas”Automatica.3013071317Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Huiling Xu
    • 1
  • Yun Zou
    • 2
  • Shengyuan Xu
    • 2
  • James Lam
    • 3
  • Qing Wang
    • 3
  1. 1.Department of Applied MathematicsNanjing University of Science and TechnologyNanjingPeople’s Republic of China
  2. 2.Department of AutomationNanjing University of Science and TechnologyNanjingPeople’s Republic of China
  3. 3.Department of Mechanical EngineeringThe University of Hong KongPokfulam RoadHong Kong

Personalised recommendations