Vietnam Journal of Mathematics

, Volume 41, Issue 3, pp 245–254 | Cite as

On Stability and Robust Stability of Linear Parameter-Varying Difference Systems with Nonnegative Matrix Coefficients

  • Bui The Anh
  • Do Cong Khanh
  • Duong Dang Xuan Thanh
Article
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Abstract

In this paper, we give a simple necessary and sufficient condition for asymptotic stability of linear parameter-varying difference systems with nonnegative matrix coefficients. Then, the complex, real, and positive stability radii of the difference systems are studied. The results also include recent results on positive homogeneous difference equations and positive delay discrete systems as special cases. Finally, a simple example is given to illustrate the obtained results.

Keywords

Parameter-varying system Asymptotic stability Stability radius Homogeneous difference equation Nonnegative matrix 

Mathematics Subject Classification (2010)

93D09 34A09 34D15 
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Notes

Acknowledgements

The authors thank the referees for their careful reading of the manuscript and insightful comments. This work was supported by Vietnam National Foundation for Science and Technology Development Grant No. 101.01-2010.15.

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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2013

Authors and Affiliations

  • Bui The Anh
    • 1
  • Do Cong Khanh
    • 2
  • Duong Dang Xuan Thanh
    • 3
  1. 1.Department of MathematicsUniversity of PedagogyHo Chi Minh CityVietnam
  2. 2.Department of Information TechnologyHCM University of TechnologyHo Chi Minh CityVietnam
  3. 3.Faculty of Math & Computer ScienceUniversity of ScienceHo Chi Minh CityVietnam

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