Canalizing Boolean mapping and its application to disturbance decoupling of Boolean control networks

The concept of canalizing Boolean function is generalized to multi-input multi-output canalizing Boolean mapping. Using the semi-tensor product of matrices and the matrix expression of logical functions, an easily verifiable condition is provided for testing whether a Boolean mapping is a canalizing Boolean mapping. Using it, the disturbance decoupling problem (DDP) of Boolean control networks is considered. A design technique is provided to produce the controls which solve the DDP. An illustrative example is presented.