Stability and $l_1$ Gain Analysis of Boolean Networks With Markovian Jump Parameters

This paper presents some results on stability and $l_1$ 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 Lyapunov theorem is derived. Moreover, an $l_1$ 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.