Robust Stability of Boolean Networks With Multiple Disturbances: An Eigenvalue-Based Approach

Stability analysis is a key topic in the study of Boolean networks (BNs). This article proposes a novel eigenvalue-based method to study the robust stability of BNs with multiple disturbances. Unlike existing stability results, this article investigates robust stability from the perspective of eigenvalues rather than the transition matrix. To demonstrate the versatility of this new method in robust stability analysis, we introduce a stochastic BN (SBN) with both stochastic sequences and Markovian jump disturbances (MJDs), which can also be viewed as an extended SBN. Subsequently, we propose an algorithm to construct the largest invariant subsets (LISs) and give an eigenvalue-based method to determine the stability of SBNs. Finally, an example is used to verify the effectiveness of the results in this article.