Induced-Equations-Based Stability Analysis and Stabilization of Markovian Jump Boolean Networks

This paper considers asymptotic stability and stabilization of Markovian jump Boolean networks (MJBNs) with s-tochastic state-dependent perturbation. By defining an augmented random variable as the product of switching signal and state variable, asymptotic stability of an MJBN with perturbation is converted into the set stability of a Markov chain (MC). Then, the concept of induced equations is proposed for an MC, and corresponding criterion is subsequently derived for the asymptotic set stability of an MC by utilizing the solutions of induced equations. This criterion can be respectively examined by eithor a series of linear programming (LP) problems or a graphical algorithm. With the help of the proposed approach, the time complexity to analyze and control MJBNs can be reduced to a certain extent. Furthermore, all time-optimal signal-based feedback controllers are designed to stabilize a MJBN towards a given target state. Finally, the feasibility of the obtained results is demonstrated by two illustrative biological examples.