Disturbance Decoupling Of Mix-valued Logic Control Networks

Mix-valued logic is a natural generalization of Boolean logic and k-valued logic. It is a new concept proposed by professor Daizhan Cheng and their research group. It plays an important role in systems control and related field, and shows its vivid life. In this paper disturbance decoupling of Boolean control networks is extended to mix-valued logic control networks by using semi-tensor product of matrices which is a new operation tool. The paper provides some new results on the disturbance decoupling of mix-valued logic control networks. First, in order to solve the disturbance decoupling problem, we define prime number regular subspace and an out put-friendly subspace. A new coordinate frame are constructed for the state space of the mix-valued logic networks. Based on the new coordinate frame we give the algebraic expression of mix-valued logic control networks. Secondly, based on the new dynamic, we establish a new procedure to deal with the disturbance decoupling problem. Finally, necessary and sufficient conditions are obtained for the solvability of disturbance decoupling problems.