Robust stability in distribution of Boolean networks under multi-bits stochastic function perturbations

Abstract

In this work, robust stability in distribution of Boolean networks (BNs) is studied under multi-bits probabilistic and markovian function perturbations. Firstly, definition of multi-bits stochastic function perturbations is given and an identification matrix is introduced to present each case. Then, by viewing each case as a switching subsystem, BNs under multi-bits stochastic function perturbations can be equivalently converted into stochastic switching systems. After constructing respective transition probability matrices which can unify multi-bits probabilistic and markovian function perturbations in a consolidated framework, robust stability in distribution can be handled. On such basis, necessary and sufficient conditions for robust stability in distribution of BNs under stochastic function perturbations are given respectively. Finally, two numerical examples are presented to verify the validity of our theoretical results.