Abstract
The paper is devoted to collecting and verifying basic facts about controllability of finite-dimensional linear continuous-time periodic (FDLCP) systems and its relationships with various Floquet factorizations. The study tries to show that reducibility and irreducibility of Floquet factorizations are a pair of unnoticed but important features about the Floquet theory. It is shown that separating Floquet factors in reducible Floquet factorizations may lead inappropriate interpretation in controllability and decomposition of FDLCP systems.
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