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Abstract We investigate the input–output decoupling problem of switched Boolean control networks (SBCNs) in this paper. Based on the matrix expression of Boolean functions, the dynamics of SBCNs are converted into an algebraic form via semi-tensor product of matrices first. Then, using the redundant variable separation technique, we give the necessary and sufficient conditions for the existence of three kinds of controllers to detect whether an SBCN can be input–output decomposed or not, respectively, including the open-loop controllers, the state feedback controllers, and the output feedback controllers. Meanwhile, a constructive procedure is presented to construct the open-loop controllers, as well as the state feedback controllers and output feedback controllers. Finally, an illustrative example is given to show that the new results obtained are effective. [ABSTRACT FROM AUTHOR]

Searching a condensed adequate set of k -valued logic is a challenging problem. Using algebraic expression of logical functions, a normal form for k -valued logic was presented in Cheng et al. [3]. Starting from the normal form, searching adequate set of k -valued logic is converted to searching set of generators of their isomorphic matrix group/semigroup. Two adequate sets of k -valued logic are revealed, which consist of only 4 logical operators: one binary and three unary operators. These two adequate sets are uniformly defined for all k ≥ 3. [ABSTRACT FROM AUTHOR]

In this paper, by applying the real representations of complex matrices, the particular structure of the real representations and the Moore–Penrose generalized inverse, we obtain the explicit expression of the minimal norm least squares Hermitian solution of the complex matrix equation A X B + C X D = E . And we also derive the minimal norm least squares Hermitian solution of the complex matrix equation A X B = E . Our proposed formulas only involve real matrices, and therefore are more effective and portable than those reported in Yuan and Liao (2014). The corresponding algorithms only perform real arithmetic which also consider the particular structure of the real representations of complex matrices. Two numerical examples are provided to demonstrate the effectiveness of our algorithms. [ABSTRACT FROM AUTHOR]