Stability and l1 Gain Analysis of Boolean Networks with Markovian Jump Parameters

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Original languageEnglish
Article number7874087
Pages (from-to)4222-4228
Journal / PublicationIEEE Transactions on Automatic Control
Issue number8
Online published8 Mar 2017
Publication statusPublished - Aug 2017


This paper presents some results on stability and l1 gain analysis of Boolean networks with Markovian jump parameters. A necessary and sufficient condition for global stability of the concerned Boolean networks is given in terms of linear programming by utilizing the semi-tensor product of matrices and some properties of linear positive systems. Then the definition of Lyapunov function for stochastic Boolean networks is presented and a Lyapunov theorem is derived. Moreover, an l1 gain problem for stochastic Boolean networks with external disturbances is formulated and solved by a sufficient condition. Examples are shown to illustrate the effectiveness of the obtained results.

Research Area(s)

  • Boolean networks (BNs), l1 gain, Markovian jump parameters, semi-tensor product (STP), stochastic Lyapunov function