Function Perturbation Impact on Robust Stability and Stabilization of Boolean Networks With Disturbances.

This article concentrates on the function perturbation impact on robust stability and robust stabilization of Boolean networks with disturbance inputs (DBNs). First, using the semi-tensor product (STP) of matrices, the algebraic representation of DBNs with function perturbation is given. Second, a state set is determined to detect the robust stability of DBNs subject to function perturbation. The result shows that the robust stability of DBNs remains unchanged if and only if the perturbed point is not in the constructed state set. Third, DBNs with control inputs (DBCNs) are considered, and several criteria to verify whether DBCNs with function perturbation can still maintain robust stabilization under a given state feedback stabilizer are presented. Finally, two examples are provided to illustrate the validity of the theoretical results.