Disturbance decoupling of mix-valued logical networks via the semi-tensor product method

This paper addresses the disturbance decoupling problem (DDP) of mix-valued logical networks by using both the semi-tensor product of matrices and the matrix expression of logical functions, and presents a number of new results on the DDP. First, in order to solve the DDP, a new algorithm is proposed to construct a kind of YY-friendly subspace for the state space of mix-valued logical networks. Second, based on the constructed YY-friendly subspace, several necessary and sufficient conditions are obtained for the existence of decoupling controllers, and a new control design procedure is established to deal with the DDP. Finally, an illustrative example is studied by the new method proposed in this paper, and two kinds of decoupling controllers are designed. The study of the illustrative example shows that the new method is effective in dealing with the DDP of mix-valued logical networks.