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

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

International Journal of Systems Science, 2019, vol. 50, issue 11, 2077-2087

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.

Date: 2019
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DOI: 10.1080/00207721.2019.1645229

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