Abstract
This study investigates some fundamental problems on regular subspaces and invariant subspaces of Boolean control networks. First, a new necessary and sufficient condition for regular subspaces is obtained, which exactly reveals the relationship between a regular subspace and its complementary subspaces. A new method to compute complementary subspaces is proposed. Second, invariant subspaces without the regularity presupposition are considered. Some necessary and sufficient conditions of invariant subspaces are given. Finally, two examples are given to illustrate the obtained theoretical results.
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