Original Disturbance Decoupling of Singular Boolean Networks: A Reduced State Transition Matrix-Based Method

Disturbance decoupling is one of the fundamental problems in control systems. This article addresses the original disturbance decoupling problem of singular Boolean networks (SBNs) from a new point of view. The robust solvability of SBNs is discussed by the truth matrix of algebraic constraints first. In order to cope with the multiple solutions, an SBN with disturbances is equivalently transformed into a switched restricted Boolean network (BN). Then utilizing a new approach based on the reduced state transition matrix, the relationship between original disturbance decoupling and robust indistinguishability is revealed, which also builds a link with robust observability. By virtue of a parameter extraction mapping, a verifiable criterion is presented for original disturbance decoupling. Moreover, our approach is still applicable to BNs and of lower computational complexity than the existing results. Finally, illustrative examples are worked out to show the effectiveness of the obtained results.