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

This paper presents some results on stability and l1gain 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 Lyapunov theorem is derived. Moreover, an l1gain 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.