Further results on dynamic-algebraic Boolean control networks

  • Sen Wang
  • Jun-E. FengEmail author
  • Yongyuan Yu
  • Jianli Zhao
Research Paper


Restricted coordinate transformation, controllability, observability and topological structures of dynamic-algebraic Boolean control networks are investigated under an assumption. Specifically, given the input-state at some point, assume that the subsequent state is certain or does not exist. First, the system can be expressed in a new form after numbering the elements in admissible set. Then, restricted coordinate transformation is raised, which allows the dimension of new coordinate frame to be different from that of the original one. The system after restricted coordinate transformation is derived in the proposed form. Afterwards, three types of incidence matrices are constructed and the results of controllability, observability and topological structures are obtained. Finally, two practical examples are shown to demonstrate the theory in this paper.


controllability dynamic-algebraic Boolean control network fixed point and cycle observability restricted coordinate transformation 



This work was supported by National Natural Science Foundation of China (Grant No. 61773371).


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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Sen Wang
    • 1
  • Jun-E. Feng
    • 1
    Email author
  • Yongyuan Yu
    • 1
  • Jianli Zhao
    • 2
  1. 1.School of MathematicsShandong UniversityJinanChina
  2. 2.School of Mathematical ScienceLiaocheng UniversityLiaochengChina

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