New Method for Disturbance Decoupling of Boolean Networks

The coordinate transformation technique is a traditional method for solving the disturbance decoupling problem (DDP) of Boolean control networks (BCNs). But under this technique, the obtained conditions are not necessary for the solvability of DDP of original systems. Thus, this article investigates the DDP of Boolean networks (BNs) and BCNs in a new perspective. Based on the new definition of disturbance decoupling, the one-step evolutionary dynamic of states of BNs, shown as a table, is presented for solving the DDP. Besides, a matrix discriminant is introduced to use MATLAB to test whether a BN is disturbance decoupled. For discussing the solvability of DDP of BCNs, a truth matrix is constructed to provide a necessary and sufficient condition and find all possible state feedback controllers. It is worth noting that the computation complexity of the main results is lower than that of the existing results. Furthermore, two examples are given to show the validity and advantages of the main results.