State Space and Subspaces

Part of the Communications and Control Engineering book series (CCE)


This chapter presents a systematic description of state spaces and subspaces of Boolean (control) networks. After defining the state space and subspaces, the coordinate transformation of Boolean (control) networks is proposed. Using coordinate transformation, some useful kinds of subspaces, including regular subspaces and invariant subspaces, are investigated in detail. Moreover, the indistinct rolling gear structure of Boolean networks is revealed. This state-space description makes a state-space approach, similar to that of the modern control theory, applicable to the analysis of Boolean networks and the synthesis of Boolean control systems. This chapter is based on Cheng and Qi (IEEE Trans. Neural. Netw. 21(4):584–594, 2010).


State Space Coordinate Transformation Invariant Subspace Coordinate Frame Boolean Network 


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