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Stability and ℓ1-gain analysis for positive 2-D Markov jump systems

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  • Yong Chen
  • Chang Zhao
  • James Lam
  • Yukang Cui
  • Ka-Wai Kwok

Abstract

This paper investigates the problems of stability and $\ell _{1} $ℓ1-gain analysis for positive 2-dimensional (2-D) Markov jump systems. The mathematical model of 2-D Markov jump systems is established based on the Roesser model. Necessary and sufficient condition for stability and sufficient condition for $\ell _{1} $ℓ1-gain computation are derived. Furthermore, the stability and $\ell _{1} $ℓ1-gain conditions are extended to Markov jump systems with partially known transition probabilities. The effectiveness of the obtained theoretical findings is verified through two numerical examples.

Suggested Citation

  • Yong Chen & Chang Zhao & James Lam & Yukang Cui & Ka-Wai Kwok, 2019. "Stability and ℓ1-gain analysis for positive 2-D Markov jump systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 50(11), pages 2077-2087, August.
    • Handle: RePEc:taf:tsysxx:v:50:y:2019:i:11:p:2077-2087
    DOI: 10.1080/00207721.2019.1645229
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