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Realization of Boolean control networks. (English) Zbl 1214.93031
Summary: Based on the linear expression of the dynamics of Boolean networks, a coordinate transformation of Boolean variables is defined. It follows that the state space coordinate transformation for the dynamics of Boolean networks is revealed. Using it, the invariant subspace for a Boolean control network is defined. Then the structure of a Boolean control network is analyzed, and the controllable and observable normal forms and the Kalman decomposition form are presented. Finally the realization problem, including minimum realization, of Boolean control networks is investigated.
MSC:
93B15Realizability of systems from input-output data
93E03General theory of stochastic systems
93B17System transformation
93B10Canonical structure of systems