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On the Connection Between the Stability of Multidimensional Positive Systems and the Stability of Switched Positive Systems

  • Hugo AlonsoEmail author
  • Paula Rocha
Chapter
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 471)

Abstract

In this work, we study the connection of the stability of multidimensional positive systems with the stability of switched positive systems. In a previous work, we showed that the stability of a multidimensional positive system implies the stability of a related switched positive system. Here, we investigate the reciprocal implication.

Keywords

Stability Switched positive systems Multidimensional positive systems 

Notes

Acknowledgements

This work was supported by FEDER funds through COMPETE – Operational Programme Factors of Competitiveness (“Programa Operacional Factores de Competitividade”) and by Portuguese funds through the Portuguese Foundation for Science and Technology (“FCT–Fundação para a Ciência e a Tecnologia”), within the project UID/MAT/04106/2013 associated with the Center for Research and Development in Mathematics and Applications (University of Aveiro) and the project POCI-01-0145-FEDER-006933 - SYSTEC - Research Center for Systems and Technologies.

References

  1. 1.
    Alonso, H., Rocha, P.: A general stability test for switched positive systems based on a multidimensional system analysis. IEEE Trans. Autom. Control 55(11), 2660–2664 (2010)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bose, N.K.: Multidimensional Systems Theory and Applications, 2nd edn. Kluwer Academic Publishers, The Netherlands (2003)Google Scholar
  3. 3.
    Fornasini, E., Valcher, M.E.: Matrix pairs in two-dimensional systems: an approach based on trace series and Hankel matrices. SIAM J. Control Optim. 33(4), 1127–1150 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Fornasini, E., Valcher, M.E.: Stability properties of a class of positive switched systems with rank one difference. Syst. Control Lett. 64, 12–19 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Gurvits, L., Shorten, R., Mason, O.: On the stability of switched positive linear systems. IEEE Trans. Autom. Control 52(6), 1099–1103 (2007)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Ooba, T.: Stabilization of multidimensional systems using local state estimators. Multidimens. Syst. Signal Process. 12, 49–61 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Ooba, T., Funahashi, Y.: On the simultaneous diagonal stability of linear discrete-time systems. Syst. Control Lett. 36, 175–180 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Sun, Y.: Stability analysis of positive switched systems via joint linear copositive Lyapunov functions. Nonlinear Anal.: Hybrid Syst. 19, 146–152 (2016)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Sun, Z., Ge., S.S.: Switched Linear Systems: Control and Design. Springer, UK (2005)Google Scholar
  10. 10.
    Valcher, M.E.: On the internal stability and asymptotic behavior of 2-D positive systems. IEEE Trans. Circuits Syst. I: Fundam. Theory Appl. 44(7), 602–613 (1997)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.CIDMA, Universidade de Aveiro, Campus Universitário de SantiagoAveiroPortugal
  2. 2.Universidade Lusófona do PortoPortoPortugal
  3. 3.SYSTEC, Faculty of EngineeringUniversity of PortoPortoPortugal

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