Cascading state-space decomposition of Boolean control networks by nested method

Boolean control networks are a kind of discrete logical dynamical systems. They are recently attracting considerable interest as computational models for genetic and cellular networks. In this paper, we investigate the cascading state-space decomposition problem for Boolean control networks by nested method. Firstly, based on the semi-tensor product of matrices, we obtain some algebraic conditions for the cascading state-space decomposition. Secondly, the multi-layer nested block matrix is defined, and two necessary and sufficient conditions are put forward based on this kind of matrices. Besides, a method is given to design controllers. Finally, an example is given to display the effectiveness of the method provided in this paper.