Abstract
In this brief, stabilization for Boolean networks ( <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">BNs</monospace> ) has been studied, based on network structure ( <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">NS</monospace> ) and pinning control ( <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PC</monospace> ). Firstly, the concept of <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">NS</monospace> for <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">BNs</monospace> is defined by searching all the relevant variables in logical functions. Then, in order to achieve global stabilization, <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PC</monospace> nodes can be determined using the concept of minimum feedback vertex set. Finally, a state feedback <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PC</monospace> is designed, where controllers are only dependent on neighbors of control nodes. The proposed <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PC</monospace> method can reduce the computational complexity and be applied to certain large biological networks.
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