On subspaces of mixed-valued logical control systems

For mixed-valued logical control systems, a necessary and sufficient condition for determining a complementary subspace of a regular subspace is obtained. A new proof of the criterion for regular subspaces is given and a new method to construct a complementary subspace is proposed. A new algorithm for constructing friendly subspaces is obtained. The concept of invariant subspace without the regularity assumption is introduced and some necessary and sufficient conditions are derived.